The Economist gives a more nuanced view [1]. Essentially saying the deterrent is independent and if support was pulled by the US that there wouldn’t be a ‘cliff edge’, which would potentially give time to replace.

The UK has produced its own nuclear weapons in the past and has weapons grade processing at Sellafield. There’s ~140 metric tons of separated plutonium stored there.

It is apparently enough material to build tens of thousands of nuclear weapons. Not every warhead has to be a billion megatons to be a deterrent.

[1] https://archive.is/Qz2lI