So, that is the question I am asking:

You are asking many questions.

Are nuclear weapons a good thing?

How so? What do you mean by good? You'll find someone who can successfully argue both sides of the coin.

Is it desirable for the UK to maintain a nuclear deterrent,

Hell yea! A nuclear deterrent increases your security. Nuclear belligerence (i.e. North Korea) is not.

or should we be pursuing nuclear disarmament?

No. It's like the firearms debate in the US. Why should the UK (one of the good guys, IMO) reduce its natural security by disarming?

Is the MAD doctrine ultimately sound, or is it dangerously naive about the risk of nuclear holocaust?

I don't believe the MAD doctrine is still in existence and was scrapped in the 1990's

Do nuclear weapons, in short, make the world a safer, or more dangerous, place?

Yes.