The UK abandoned it's independent rocket making capability with the cancellation of the Blue Streak project in the 60s, opting (after another US system they intended to purchase was also cancelled) to buy US Polaris missiles and manufacture the warheads in the UK instead.
We now have Trident missiles bought under pretty much the same arrangement; because IIRC the UK is pretty much reliant upon US maintenance not just to maintain the missiles, but also the warheads (Uk uses a copy of a US warhead design, I believe), it's basically a system completely reliant upon US co-operation and technology. If the US decide not to play ball (say they want an early warning radar station for that completely ineffectual 'son of star wars'), they can withdraw support and paralyse British ICBMs. (I'm not sure on the situation with bombs, etc)
This is a system which costs over £250m per year to maintain, and will cost tens of billions in the alread-approved upgrade (including aforesaid warhead factory), not to mention that it may violate non-profiliferation treaties.
That amount of money, of course, could be used in sooo many more useful ways, even within the military (perhaps actually giving them boots, body armour and proper desert camo for our next desert adventure?).