The EU won't get our membership fee so the others, who are in massive debt will have to pay more. They will not get our 60 billion trade if they refuse us a deal - the EU is stagnating and losing its share of world GDP year on year. The EZ is a basket case and many within the EU are not happy with it and want change. The cards would staked against them and they would crack up. If the EU does then the global market will too.
They, the world, have no choice but to be nice to us.
If you had listened to those 'More or less' broadcasts you would realise that:
A/ There will be no massive 'windfall' from ending our EU subscription.
B/ The size of that payment is small compared to the benefits of membership.
The EU market is still one of the largest and most important in the world, we can't afford to turn our back on it!
The world is not going to come rushing to our rescue if we get ourselves in deep shit.