I think the reality of this is a little more nuanced. By virtue of geography (it's an island) Britain was the last place Germany were able to overrun. This bought time for what remained of the European forces to gather and reorganise, and provided a staging point for further counter-attacks.
The fact is, that Britain has never been invaded, not in modern times anyway, and outside of bombing raids has never known the true humiliation of hearing the foreign powers' jackboot marching down the street.
Just about every other nation in Europe has, and understands the value of the peace that closer union brings about.
>.. but lost the war.
Ultimately being able to claim "they won the war" may have done the UK more harm than good because they were never incentivised to address their deep deep social issues in any kind of a constructive way.
The good that comes out of the brexit fiasco might be that this is an eventual turning point for them.