Don't worry, there will be a Trident replacement. If the Government got rid of the nuclear deterent, it would lose its place on the UN Security Council. They would not countinence that, so there will be an update...
I'm afraid you've been hooked by one of the biggest urban myths out there.
The UK is not just a member of the UN Security Council but a
permanent member of said security council, and the permanent members set themselves up quite a little cartel when it was formed.
In order for a permanent member of the UN Security Council to be voted off
all current members must agree to it in a vote. As the UK has the power of veto any vote taken would fail unless the UK voted itself off. The words 'turkey', 'voting' and 'Christmas' might be apt here.
Ownership of nuclear weapons is not what gained the UK its place as a permanent member, rather its place was gained by being one of the 5 major allied powers at the end of the second world war. The fact all the permanent members have nuclear weapons is a 'happy' coincidence that came about by being the major nations involved in the Cold War.