Given that the nukes that the UK has is Trident, which is a US system that the UK cannot use without US cooperation [0], it seems entirely appropriate that the USA gets to decide if the UK has nukes.
[0] Yes, the UK can fire them without US approval, but the actual hardware is maintained and supported by the USA, and they have to be shipped to the USA regularly for maintenance. If the USA decided that the UK should not have nukes, there's not a lot the UK could do about it, the Trident system would have to be scrapped entirely and replaced with some completely different system. Which the UK doesn't really have the capability to do and it would cost a fortune to acquire that capability.
That's only the delivery method, the warheads are UK-designed and built.
So yes, if the US withdrew support then the existing nuclear program would be pretty fucked for a while, but the US couldn't unilaterally de-nuclearise the UK.
Who else on the planet would have the effective power to possibly even think about who should and shouldn't have them, while plausibly being able to do anything about it?
Then you're in no position to throw rocks. The US is currently humiliating itself on the world stage in a fashion that makes Brexit look positively sage in comparison.
Given how the situations w.r.t Ukraine & Iran escalated, the US is the only country that has specifically and publicly demonstrated it's inability on both counts.
We can't give Ukraine their nukes back because they were decommissioned (and they were rotting at the time), but there'd be no nation more deserving.
Corollary: no individual nation is able to shoulder such responsibilities.
[0] Yes, the UK can fire them without US approval, but the actual hardware is maintained and supported by the USA, and they have to be shipped to the USA regularly for maintenance. If the USA decided that the UK should not have nukes, there's not a lot the UK could do about it, the Trident system would have to be scrapped entirely and replaced with some completely different system. Which the UK doesn't really have the capability to do and it would cost a fortune to acquire that capability.