The cost of renewing Trident will be about $40 billion over the next decade, according to the military itself.
This is a whopping amount of money from our coffers to American ones.
More than that, what a lot of people don't know (aren't told, really) is how nuclear 'obsolescence' works. Warheads don't have an expiry date. What obsolescence means to say is that some of the countries with the best defensive technology might be able to stop the nuke getting through.
In other words, unless we want to pay $40b to maintain the guaranteed capability to fire nukes on Russia, China, or, er... America (maybe that last one's not so bad JK), it's a big bill which I genuinely don't see the need for. Especially 'cause, sure, with Trident we could probably take out St. Petersburg, or Guangzhou or even Washington D.C. But then when their capability comes as a counter-attack, we're completely ****ed.
I'm not even suggesting that we necessarily stop the $40b going through to military purposes. But Trident's still perfectly effective for if we want to blow up Daesh, or Kim Jong-Un. Meanwhile, you could spend that money on much better armour and personnel vehicles (ours are abysmal!) and on getting some of the troops back on the pay-roll. You know, some of the ~35% that Hunger Chancellor Osborne, without warning or given reason, laid off (I wonder how many top admirals got laid off? None most likely).
Edit: to answer the above, although we do maintain the right as to this being our own independent weapon, it IS true (admittedly according to my Dad, who probably thinks there's fairies at the bottom of the garden after his customary bottle of wine) that we've not once fired any kind of major explosive at co-ordinates the Yanks haven't provided to us. Don't get me wrong, they were a good target to hit for both of us, but it remains a bit of a cringe system: buy weapons from the Americans, fire weapons at targets they appreciate us doing so, buy more weapons from the Americans.