I too wonder wether the effects will be as disastrous as many say they will be. For your bunq-account nothing will change in the short run as (as far as I can see) the UK will still reside within the European Economic Area and citizens of EEA-countries are eligible for opening (or maintaining) an account at bunq (exceptions aside, but they don't include the UK).
As you already said, it isn't likely that the UK government will ban foreign banks immediately on March 29th as that would mean (more) economic suicide for Britain than the whole Brexit-idea. It is likely however that London will restrict international banking in the upcoming years as they have no restraint to protect their domestic economy against cash drains to the continent. As the pound sterling isn't the toughest guy in the classroom anymore (it used to be in the days Dad's Army was still new and the Beatles were together), it needs domestic protection by the British government against consumer investments in other currencies like the euro (consumers seeking for a save harbor for their money in times of devaluation).
If I were you, I would take a slightly secure approach towards the Brexit-developments. In the unlikely event Downing Street panics and imposes sudden restrictions on acces to foreign assets (which effectively bunq is as bunq is Dutch), be sure to have some petty cash on your domestic account to get you through the first weeks. For the rest: enjoy bunq as long as you can and don't worry. The stakes are too high for the British government to create too big of a fuzz on this matter.