It's use would bring destruction to all those involved. Other countries have given up nuclear weapons and it's not like anyone has taken them out with nukes.
The UK is still considered a "Great Power" by just having the fifth largest economy, and nuclear disarmament wouldn't diminish this - in fact it would bring economic benefits by recouping the social wealth that goes into the black hole of nuclear weaponry.
Would he dare reverse so long-standing a policy? Is this the kind of bold but popular move that would be the thing to reinvigorate Labour standings in the polls? I can't see much else getting them back up in time for the nexr election.
It would give him a bump in popularity, but it wouldn't be sustained unless he took other progressive-popular steps too. I don't really think he's got the political bottle to do it. It would be interesting to see Labour bringing an anti-nuclear facet to a General Election manifesto which would have Davey Cameron umming and ahhing over his 'commitment' to green-populism. Cameron would have difficulty matching policy as the Tory right wouldn't be having it.