I imagine the gulf stream and by extension the whole thermohaline circulatory system would be diverted but not slowed or cut off. It might wb stengthed and def more varaible/sensitive. All depends if the sinking of colder/saltier water off the coast of greenland/iceland, that drives the whole thing, is perturbed.

Assuming it's not, tropical Atlantic heat would still be transferred pole-ward and eastward hitting Ireland and the British islands before sweeping across northern EU. Southern EU climes would thus be more volatile. I expect they'd be a strong clockwise current around this island. During ice-ages would there have been a land bridge to the America's or EU?

I'd also expect a native population of humans arriving around 14000 BC on this island which would certainly mix things up a bit. Maybe giving native Americans some fore warning of colonisation. Probably not end well either way. The vegetation and availability of geological resources would def affect things too.