A lucid post from Prof Mark Elliott of the University of Cambridge of
where we are post-Brexit, from a political and constitutional point of view. The whole post is worth a read, but I will reproduce a section as it is pertinent to the topic immediately under discussion.
Third, the likelihood, therefore, is that Brexit will be accomplished under Article 50. That means that — unless matters are wrapped up earlier by mutual agreement — the UK will remain a Member State of the EU for at least two years from the date on which notice of the UK’s intention to leave is served upon the European Council. And that gives rise to the question whether — and, if so, when — notice must be served. As a matter of law, notice does not have to be served — ever — because the outcome of the referendum is not legally binding. The legislation that provided for a referendum to be held said nothing whatever about the effect of the outcome of the referendum, and the result does not place the Government under any legal obligation to secure Brexit — whether by serving notice on the European Council under Article 50 or otherwise. Put another way, the United Kingdom has not, simply by holding an advisory referendum, “decide[d] to withdraw” within the meaning of Article 50. Rather, the will of the people has been expressed through an advisory referendum, and the making of the decision whether to withdraw remains a matter for the Government.
However, to say that the Government is not legally obliged to trigger Brexit is one thing. Political reality is something else entirely. It would, self-evidently, be astonishingly political difficult for the Government to ignore the outcome of the referendum, and there is, in effect, an insuperable political obligation to fire the Article 50 starting-gun. That does not, however, mean that the UK Government must — or should — immediately do so. Given that it is not obliged by UK law or by EU law to start the Article 50 process, it can, if it wishes, bide its time — in order, if nothing else, to take stock and work out who, and by reference to what strategy, the negotiations will be conducted. The UK could, for instance, decline to trigger the Article 50 process until a new Prime Minister takes office in the autumn — which is what David Cameron appeared to envisage would happen in his resignation statement.
The rest of the post also states that EU law continues to apply to the UK until the end of the period envisaged by Article 50 (which could be longer or shorter than two years with the agreement of all 28 current Member-states). As the UK-EU deal only came into force if the UK voted to remain, that means that it is practically guaranteed for there to be no change to the EEA-Route Applications for the next two years at least. I can imagine that a lot of you would be relieved by that development.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.