If the MPs go against the will of the people there would be protests; and in extreme times violence, on the streets.
I think you are also missing one further crucial point.
Prior to the referendum (which of course forced people to concern themselves with the EU) the EU was a non-issue for the vast majority of people in the UK. Sure there have been a tiny minority of anti-EU fanatics, but they are just that - a tiny minority. Most people, for most of the time, are concerned about the economy, the state of the NHS, schools, terrorism etc.
There is a very longstanding MORI poll on issues of importance to people - it is unprompted, meaning people can mention anything that concerns them. This has been run for decades and guess what, the EU hardly makes a blip on the list of issues.
I think you are projecting your view onto others - just because your are totally obsessed with the EU, it doesn't mean that most people are - they aren't, most people couldn't have given a hoot about the EU, but because of Cameron needing to pander to his frothing cabal of euronutters, he forced everyone to have to take a view. A stupid idea that we will regret for decades.