Yes. Because the alternative -- which we are currently seeing unfold -- is a wave of sovereign default, starting with the PIIGS and ultimately taking out the USD as the world's reserve currency.
...I should add that Northern Rock did not have to be nationalized, nor should taxpayers be obliged to pay any kind of compensation bill. Bankruptcies can and must happen to clean out the dead wood.
UK law provides taxpayer backed guarantees to a fixed balance per saver per bank; if NR had been allowed to collapse the UK taxpayer would've been on the hook for that amount.
And I agree that bankrupticies must be possible and are a good thing for businesses as a whole; Too Big To Fail explicitly works against this. NR was big enough regioinally that it'd have caused major economic damage to that (already fragile) region had it been allowed to go down.
...I should add that Northern Rock did not have to be nationalized, nor should taxpayers be obliged to pay any kind of compensation bill. Bankruptcies can and must happen to clean out the dead wood.