No. The best thing this country could do for itself is rightsize itself.
What does that even mean?
It means that we should no longer pretend to be a big player. Give up Security Council seat, accept that there is no "Special Relationship" (except when it suits the Americans), stop joining in pointless, unwinable wars and get rid of a nuclear deterrent which costs a huge amount of money that could be better spent.
And let France be the only nuclear power in Europe? Is that what you are saying?
The important word in the poll question is 'deterrent' - if our nuclear arsenal really were a deterrent I would unreservedly vote yes - the simple fact though is that it isn't.
We have insufficient weapons for it to be a real deterrent and even if we increased the number held they would/could never be used without the assent of the USA.
Our current 'nuclear deterrent' is nothing more than a vanity project that costs a fortune.
So if, say, US politics undertook a change in direction and they went empire building, and decided that they wanted to make the UK a part of their empire (a sort of servant becoming the master thing) would we be able to stop them or simply deter them from doing that with only conventional weapons? (* not saying that they ever would try it) the threat of nukes would surely help prevent this should something similar ever happen.
Get rid of ours and you could have countries like North Korea and other less stable countries developing and getting their own nukes could shift the balance of world power and threaten us too (think of it as the old adage of a knife beats a fist but a gun beats a knife and so on upto nukes, if they have them and we don't, arn't we more likely to have to give in to their demands- - the US can't take on everyone)
Get rid of ours and rely solely on the US and we could potentially become a bit of a puppet on a string to them and could give them greater say in how we run our own country (do things in a certain way or we won't defend you) Nuclear weapons have had a stablising effect on large areas of the world like Europe because without them, the 2nd world war could have very well continued and Russia may have gone on a land grab across Europe, replacing the power vacuum left by the Nazis when a lot of countries wouldn't have been able to put up a lot of resistance (we were dismantling, the US withdrew back to the Pacific / US)
Also, how do you stop undesirable countries from developing their own nukes, by having the threat of destruction if they were to try it and nukes make it more likely that they will cave in and back down rather than risk a war because they know that they can't win that war where they may have been able to do better with a more conventional conflict