Yes, they have four (4) nuclear ballistic submarines with Trident D2 missiles on it.
I doubt they keep them bottled up in the Atlantic. I would bet one is in the Indian or Med. Oceans.
I would also bet that they can still deliver air-to-ground nukes (B51/W53 bombs) still in inventory.
The UK did away with its free fall nukes back in 1998. The last operator of the UK produced WE177s was the RAF Tornado fleet. The only nukes in UK service are with the Royal Navy's submarine launched ballistic missile fleet.