The one that's in dock for service and repair, yes. But the others could be at sea anywhere in the world, in an unknown location.
> Would all four, if armed, be able to do much damage back?
Each sub can carry 16 x Trident D5 ballistic missiles, with a range of 6,000 mi. Each missile carries multiple warheads, each with much higher yields than those used at Hiroshima and Nagasaki. So certainly the potential to do lots of damage.
The US has a similar setup with their Ohio-class submarines, though I don't believe they carry such letters or equivalent.
For a "last resort" use like this, counterforce (i.e. attacking the enemy's military) is probably pointless. I imagine you'd go for cities if you wanted to cause as much hurt as possible.
A single 100kt warhead detonated over, for example, Manhattan would devastate Manhattan and significantly damage surrounding areas. Deaths would probably be in the millions. Add in a few more scattered around intelligently and that's the entire metro region wrecked. If we figure four is enough to do NYC in decently, that means one of these submarines could wreck twelve cities that way. More (up to 48) if you just wanted to smash the core areas. Or you can mix and match.
If it was targeted at the US (don't ask me why), imagine DC, NYC, LA, Chicago, all completely flattened, along with a bunch more. Most of the population of the country as a whole would survive, but the country itself would be pretty thoroughly wrecked.
(In case anyone is wondering what the difference is, a cruise missile is basically a suicidal unmanned drone that flies like an airplane, while an ICBM is a rocket that goes into space and then falls back down on its target after burning its fuel.)
Whether these are in the form of sealed handwritten letters from the President, I don't know.
To get some idea of the likely outcome of a nuclear war for the UK I can suggest watching Threads:
http://en.wikipedia.org/wiki/Threads
One interesting thing about Threads is that it is based on a rather optimistic attack scenario based on an exercise called Square Leg:
As a "Yes" voter I'm hoping we'll be able to send them back to England, preferably somewhere on the south coast.
And I am sure that some of the depressed areas of southern England woudl welcome these jobs with open arms - theres already suspicion that English dock workers where made redundant to protect Scottish jobs.
http://en.wikipedia.org/wiki/Argyll_and_Bute_%28Scottish_Par...
The MOD itself says that a total of only 520 civilian jobs would be lost if Trident was moved - and only 310 of those are definitely locals:
http://www.heraldscotland.com/politics/political-news/labour...
And finally, don't you think some things are more important than money and jobs?
I really liked Charlie Stross's account of how he changed his views on an "independent" nuclear deterrent:
http://www.antipope.org/charlie/blog-static/2013/04/on-the-u...
Personally, I changed my mind from being a reluctant supporter for the need for nuclear weapons while wandering round, of all places, Auschwitz-Birkenau, our guide made a comment about how although Auschwitz-Birkenau remains the very worst that we have achieved as as species a lot of countries, including the UK, calmly contemplate the use of weapons that would have far worse results. From that day I have felt very strongly about trying to remove nuclear weapons from my country and independence seems the most viable route to achieving that goal.
No. The idea of ballistic missile submarines like this (and those also operated by the US, France and Russia) is that they should be impossible to find when on patrol.
http://en.wikipedia.org/wiki/HMS_Vanguard_and_Le_Triomphant_...
A US missile submarine also collided with a Russian attack submarine in 1992:
http://en.wikipedia.org/wiki/Submarine_Incident_off_Kildin_i...
'Hervé Morin, France's Minister of Defence, said that they "face an extremely simple technological problem, which is that these submarines are not detectable".'