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Not quite. The hose on the pump wouldn't release when there was any pressure in the tube. It would lock on. Unscrewing the pump from the hose would release all the air out of the tube. Even without pressure in the tube the hose wouldn't come off until I'd walked about two miles with it hanging onto the valve and tried again.
I then got another puncture in Elephant and Castle without a working pump. More walking yay!
Safe to say, one of the first things I did today was order a new pump.
@jaeyukdapbap Was it a valve core unscrewing in the pump? The self rescue technique in this situation is to stuff the tyre with grass and ride slowly and carefully to the nearest pub/station/taxi rank.