I'd prefer four not three. In fact five would make me feel more comfortable. My logic being that if you are spending £20 billion on a national strategic deterrent you might as well spend the extra few billion on a couple more boats to carry it as it is a bit silly to have said deterrent temporarily disabled if one of them has a crash and needs repairing - the total of four boats was always said to be the minimum needed to guarantee keeping one at sea all the time.
Though in fact I still haven't got over the abandonment of the "two power standard" for setting the size of the Royal Navy in 1912 i.e. equal to the next two biggest navies combined (some typical Liberal Minister called Churchill was running the Admiralty then).
I don't buy the "contributing to multilateral disarmament" argument. No one took any notice, let alone cut their own arsenals, when Blair cut the number of warheads from 200 to 160.
I would be interested to know why France considers it needs and can afford 300 warheads carried by a combination of four SSBNs and 60 airplane-launched nuclear missiles for its force de frappe. Maybe they anticipate someone being a future strategic threat that we don't.