https://cnduk.org/resources/trident-us-connection/

Trident is reliant on the US. Without approval from Washington, the UK could not use its nuclear weapons system.

https://en.wikipedia.org/wiki/Trident_(UK_nuclear_programme)

(UK government think tank source) https://www.chathamhouse.org/2025/03/uks-nuclear-deterrent-relies-us-support-there-are-no-other-easy-alternatives

Unlike most US allies in NATO, the UK is officially a nuclear weapons state, and therefore less reliant on Washington’s nuclear extended deterrence guarantee. It has its own nuclear weapons system, Trident, which is based in Britain and ostensibly operates independently.

However, Trident is closely linked to the US’s nuclear programme, raising concerns about its independence. The missiles are US-built, and the system relies on the US for maintenance.

As said ostensibly only the prime minster has to give approval to use Trident, however in reality because most of the system is built whole or in part by the US they are required for it's continuous upkeep to be operational and could remotely, or from their bases in the UK, prevent them from working sorry for the reddit comment link the info contained therein is in the legit sources I posted and others but this comment puts it succinctly if you don't feel like trudging through a lot of technical info)