I've heard claims that the gulf stream switching off would cause Britain to undergo a climate change that would have consequences I would call 'catastrophic', at least in the short term. Some predictions talk about average temperatures dropping by 5-8 C in a matter of months which would have severe consequences for British agriculture and would likely have a noticeable impact on GDP. I'm not sure I put much faith in those predictions however.

This would also be a catastrophe on a different scale from the more alarmist AGW predictions. We're talking about a major disruption to the British economy but not an existential threat to the human race.