There are many skills that a person might like to develop throughout his/her life for many different purposes, such as a hobby, or for low level application for relative independence (such as learning basic use of tools as to not need to hire an overpriced handyman for small fixes), or to gain perspective into the world of those who master any one sill (such as painting or dancing or athletics), or as a complimentary skill to a bigger, more important skill (such as improving your vertical jump can improve your headers in soccer, without the need of becoming an Olympic high jumper). Language feels different though. You can't even follow a TV series in English, by learning some English and turning on the English subtitles. You need to switch language settings and thus lose much of the essence of the show. So, what possible purpose can there be for learning just a bit of a language, other than wanting to know how to order a beer while traveling? But even then, nowadays, for that we may just go to google translate. Language is for communicating, and unless you learn it with the intent of being able to communicate, whether as the receptor of information, the one sharing, or both, what is the point? Assuming that this perspective (of learning language in such a way that communication is truly possible) is true, then a student needs to be presented with real life learning scenarios, and what is the most successful real-life learning scenario of language? I would say that from the learning of the native tongue. Full uninterrupted immersion. 
What is this scenario like? ... because native speakers can communicate with everyone around them. If presented with a person of same language but different accent, culture, or nationality, they can perceive enough through context clues to zero in on the differences, and therefore the meaning of what they were being told. Therefore, the case must be that the methods to gain the first language must be effective. Of course there is the factor of being immersed for years. But after a first language is acquired you gain a foundation for the entire concept of language, which should absolutely accelerate the SLA (although relying on this L1 base could also demotivate if the L2 is of a completely different birth such as Latins vs. any oriental language). So how can we make use of this idea to apply it into a teacher's personal plan of execution for teaching English?

Well SLA is true when it is firmly set into a student's subconscious. When a student can gather information from subconscious listening, it must be a sign that he has a considerable grip on the language. But personally I would not do much about testing this in a student, nor would I get over-interesting in my teaching approach. I trust that the most natural approaches usually keep a student progressing and interested. So how:
Basic vocab, nailing structure, Cognates, semantic fields, more cognates, and dialogue based on relatable topics. Constantly speaking, constantly listening. 
Why basic vocab and cognates? If I want to give a student a chance to immerse him/herself into a language I would want this student to have a database to search through to feel like there's something to go to to attempt speaking, and deciphering what they heard. Cognates are surprisingly vast. It seems that the more 'formal' a word, the more likely it is to be shared by many languages, ESPECIALLY languages that happen to have similar roots. With a sizable database of words and some basic structure the student might feel like he has English-speaking ability, and thus automatically getting a boost in confidence and motivation. Once the student has enough to defend him/herself with in a conversation I would expand on their vocabulary by getting to semantic fields of words that seem most relevant to their specific interest; like creating strings of information of subjects that seem most interesting to them, rather than separate chaotic units that could only overwhelm them. Everything in my curriculum would be creating a foundation for dialoguing. Through dialogues the students' would constantly apply what is already in their foundation and adding onto it, by branching out from what already is in the foundation, expanding; all while gradually adding different tenses. 
The uniqueness of the student would come in mainly in the form of 'which topics do I decide on for the semantic fields and dialogues'. For example if it a teen boy, a topic that could hardly fail to gain his interest is sports. Teaching him all the verbs associated with sports, and the surrounding nouns and adjectives and adverbs already would create a meaningful repertoir of vocabulary. Learning to apply it by speaking of what 'Messi did last night', 'how long he will have been doing it for', 'where he will be in a few years', ' what he is currently doing to stay in shape to improve', etc, would be a way of offering repetition to the use of different tenses, and surely registering in his subconscious the use of these. All because it is such a familiar topic, will the student be able to firmly grasp the otherwise complex use and variety of syntax structure. For the case of this young boy, sports analysis often uses inversion and passive voice, which would offer the teacher an activity to search for, or even create for this purpose. 
And always, always, finding a way to help the student notice his progress; to help him seen that he is a long way from where he started, and therefore his time is worth spending with this teacher. Motivation, and confidence. Always.
Syllabus. A proper syllabus organization is an indispensable guide to observing progress. Without a syllabus a teacher will not know where the student fell of the ship, or where to adjust to if a student leaps in progress. A syllabus is the tool for maintaining and adjusting pace. Since language is so limitless, as far as vocabulary and topics... I wouldn't stress too much. Basically it's all about student's preference. My syllabus would progress in the direction of complexity of tenses at first, always integrating interrogative form, conditionals along with auxiliary and modal verbs, moving on to formal voices, some phrasal verbs, proverbs and idioms, expanding on phrasal verbs again, and everything that falls in between to make language possible. 
Briefly summarizing about a teacher's role in the classroom, I've spoken about a method, but what should be the day to day approach? A teacher's lesson planning is very important, as it is necessary for the teacher to show confidence in his/her material for the student to feel confident that he/she's with the right person to reach his/her goals. This means, in the case of Oxbridge where the material is preselected for the teacher, that the teacher shall study the material offered to teach to a degree of manipulability. He shall know what is the goal of each activity so that he can improvise enough to remain genuine, personable, while also staying in line with reaching the purpose. It isn't about babysitting in the student's L2, there is an objective to go after, but it needs to be done with humanity. Again, the most natural way, the native language's way (unless some of my reader's learned in a rough way... I apologize if that's the case). And while the target is for natural dialogue, the student needs to be the speaker for about 65-80% of the time. Teacher's attitude, preparation and material selection is a matter of professionalism. We are all in this to 'put food on the table' but it is important to be considerate of whoever is investing in the learning of the student; whether it is a boss, a parent, or the student him/herself. Therefore, a teacher should prepare sufficiently so that the class may go fluidly while with purpose, material selection that connects with the student, but above all an attitude that invites the student to be there in the present moment, not waiting for whatever is next in their day.
Oxbridge is the method, the teacher is the approach, and together they should guide students to feeling confident in their English-speaking abilities. 
Nothing new. Teaching has one variable that should be a constant. A teacher that takes interest in the student/s. The future of teaching will get complex, always integrating new technologies, and fresher developments in the psychological and sociological fields; but I believe in the Oxbridge philosophy, which seem more like returning to the roots. Just conversing. The future of learning teaching should lie in humanizing the concept. People aren't robots, we don't only toss information around and gather. Which tools we use for learning aren't as important as what the learning experience is like. Learning tools can only be complimentary, not of primary relevance. We have areas of interest, we have emotions, and relationships, and these all can be distractions or tools for teaching. We should develop teachers conscious of consciousness and use this to steer the student into not only learning the language faster, but also becoming more confident people in their own skin. A teacher will teach  best if he can connect with the students inner child, whether child or adult.
I want students to learn in the quickest most well rounded fashion. Grammar and vocab, applying these through discussion (speaking and listening) in topics where they feel most familiar or related or interested. Which materials to use feels of secondary relevance at best, while visuals are actually very helpful, to make neural correlations. My syllabus would absolutely be across the board situation-based, but structured in a periodical coordination of structure/lexical/dialogue based lesson planning. Students will improve vocab and structure, use them in dialogue, and be tested in their handling of real life situations where the target vocab is necessary, and obviously observed through dialogue. Such as a day learning vocabulary of kitchen materials, learning tense structures in future continuous, past simple, with verbs in a cooking and eating scenario (such as cook, pass, stir, add, toss, eat, swallow, etc) and finalizing with a simulation of a parent-child, or server-client dialogue. Teachers can evolve by taking interest in their vision, and progressing with trial and error with intention. Testing new methods with different individuals. Remaining engaged, without their patience shaking. 
And lastly, the educators' collaboration. Typically we only fully relate to our experience, which is where our perspective comes from. In oxbridge there is a web of teachers accumulating personal experience. The more a teacher takes interest in another teacher's experience, the more a teacher can expand his perspective to a more encompassing planning/execution approach.