Those SSBNs aren't that old, either. Saying they'll be obselete in 2020 is basically saying that the House of Commons is unwilling to pay for a mid-life refit, but is willing to expend vastly greater sums of money to build a totally new class of SSBN.
What, you were expecting them to think rationally?
The rank-and-file of the RN is convinced (probably correctly) that saying "Oh, there are no threats now, there won't be in 20 years" is downright idiotic, and it would be a good idea to plan to have a viable nuclear deterrent in 2020 and beyond. However, the RN also has a major fear that some lunatic will convince people they should design and build a new class instead of just paying for the damn mid-life refits on the Tridents and it will take precedence over (and kill) the RN's carrier program. There was an article about it by an RN Captain in this month's Proceedings issue.
And saying that the UK no longer faces threats from any other nuclear-armed nation...let me put it to you this way: in 1996, a Russian SSBN captain was quoted as saying his missiles' default targeting packages had not changed since the late '70s. Another was quoted in 2005 as saying the same thing. The Cold War is over, sure. The missiles on both sides are still pointed in the same direction. Granted it's only a default setting, and can be changed easily. But the default setting on Russian missiles still includes targets in the UK. As long as this is true, an independant nuclear deterrent is something you're probably going to want.