One of four British Vanguard Class SSBN - at its Scottish base area (from UK DailyMail).
The UK Trident missile system on the current Vanguard submarine platform (from UK DailyMail).
A British Royal Navy Tomahawk Cruise missile - which may replace UK Trident - or more likely a mixed Trident ballistic and cruise missiles on each sub solution..
The UK has been unable to decide for the last decade or so whether it will replace its Trident SLBMs (its only current SSBN missiles) with an updated SSBN of 3 or 4 subs. The UK might choose nuclear tipped cruise missiles as the new deterrent or a combination of Trident and cruise. Fortunately US Multiple All-Up-Round Canister (MAC) technology could provide for each Trident tube to carry a Trident ballistic missile (with several MIRV'd warhead) or up to 7 Tomahawk cruise missiles.
The issue of Britain's post Vanguard SSBN nuclear armed submarines is naturally an issue for the Royal Navy, Ministry of Defence, UK financial departments, shipyards, unions and pacifists. Many pacifists argue for no replacement SSBNs or Tomahawk cruise only.
Concerning ballistic missiles vs cruise, the UK Ministry of Defence appears to primarily rely on the alleged technical disadvantages of cruise (in terms of payload, range, speed and vulnerability) compared to ballistic missiles - see The Future of United Kingdom's Nuclear Deterrent (Trident White Paper) 2006, page 25 http://www.mod.uk/nr/rdonlyres/ac00dd79-76d6-4fe3-91a1-6a56b03c092f/0/defencewhitepaper2006_cm6994.pdf .
I've conjured up the scenario of a first strike by Britain against a nuclear enemy to highlight the downsides of cruise. Speed (in a first strike scenario - say against Russia, China or a nuclear armed Iran) might be the most compelling issue. If a ballistic missile armed enemy detects a UK cruise missile attack early on (say by satellite infrared detection or signals traffic analysis) - the enemy may be able to launch and complete a second strike even before the UK cruise missiles have hit their targets.
The risk exists that UK cruise would arrive too late, destroying, the enemy's now empty missile silos and truck/train mobile launchers. The enemy (particularly an efficient Russia or China with S-400 SAMs) may also have shot down a significant number of UK cruise.
Trident also permits rapid multiplication of a nuclear warheads by producing theoretically up to 12 MIRVs (or a mix of MIRVs and decoys) per Trident missile. While cruise's are very stealthy they can't split into MIRVs.
Another problem with cruise is the inherent ambiguity of that missile mode with both nuclear and conventional traditions. The enemy may not know whether a UK cruise missile attack consists of all nuclear, some non-nuclear WMD, all conventionally armed warheads or a mixture. An enemy may therefore cover all UK cruise possibilities with a nuclear response against UK targets.
An untrustworthy future Iran may also work on a nuclear missile use them or lose them basis due to Iran's likely relatively small number of ballistic missiles within the next two decades. Hence any US, UK, Israeli, or French concept that conventional weapons are "safer" when used against a nuclear state may all go horribly wrong and lead to nuclear retaliation by that state (especially a newly nuclear armed state that has only "narrow" nuclear options).
The deterrent "benefit" of nuclear MAD also becomes more complex if conventional, or non-nuclear WMD's make uncertain the 'comfortable certainties' of nuclear MAD.