The problem with a deterrent force is that it's impossible to prove if it is working or if it ever worked.
Fact - the UK V-Bomber/Polaris/Trident has been in service for around 70 years.
Fact - the UK has never been invaded nor been in a major war in that time.
Theory - the two are 100% connected.
Problem - lots of other things have been in place defence -wise over the last 60 years - membership of NATO for example - which may also have stopped a serious war.
Dilemma - if the UK scraps its deterrent force does this mean it is more likely to be in a major war going forward? It could be that it WAS a major item. or it could be that it wasn't but MIGHT be if the USA decides to disengage going forward. Or maybe it is a total waste of time or money.
A college lecturer of mine used to compare this sort of debate to the Aztecs absolute belief that if they didn't sacrifice people the world would end. It's easy to say "stop it" but it's seen as a terminal risk by those involved in policy and they know who'll be held responsible if they are wrong.
It's a matter of judgement and balance - personally I believe it probably isn't a real deterrent and it is a major distorting factor in UK military finance and procurement - but I can see why so many people go for the status quo.
It's not a "flag-waving" or a "flag-burning" issue TBH - it's a honest difference in strategy and belief - that can only be solved in a democracy by the elected politicians - whoever they are.