Referendums can often give a government an instruction that its ministers believe will be difficult to carry out. There is advice on how to handle this from a former Danish minister—here. [Shorter version: you can do what is in the country’s interests once you’ve exhausted every other acceptable possibility].
I don’t believe that any serious observer doesn’t at least suspect that Brexit will be a disaster for the UK and there may come a point where the downsides are so obvious and vast that the UK will try to throw the engine into reverse.