The effect of the Gulf Stream on European climate isn't as large as often made out to be. The simple fact that Europe is on the western side of a continental landmass accounts for a huge portion of its climate - air travelling west to east over the ocean absorbs warm moisture and heats up, as the wind travels east across land it sheds that moisture via rain and becomes dryer and colder.

It's one of the reasons why Vancouver and London have similar climates, and both never get as cold as either of New York or Vladivostok, both of which are to the south of them.