There are two currents responsible. The first ocean Current is called the 'North Atlantic Drift' (not the Gulf Stream - the North Atlantic Drift is a continuation of it). It flows from 300 miles west from New York to Europe at less than 5 miles an hour (measured by boats and satellites). It is a warm current as it raises temperatures.

There are various causes of ocean currents. The North Atlantic Drift is caused by strong South-West winds in the Gulf of Mexico. A Mediterranean current is caused by differences in salinity.

But why should a flow of water so cold in winter it would kill anyone in it for more than a few minutes responsible for high temperatures in Europe. The reason is that water is a super reservoir of heat. It can be heated to a deeper depth than land has a high specific heat capacity (takes a lot of heat to raise its temperature). On the coasts of Europe this heat is released and carried towards land by the South Westerly prevailing winds. These warm the winds raise the temperatures of Western Europe. If you happen to swim in the sea (at Bournemouth) and swallow some sea water (not recommended) you will notice how remarkably salty the water is. Although all sea water is salty it is especially so as it was transported from the Gulf of Mexico by the North Atlantic Drift.

Newfoundland is made even colder by a cold current. It is called the Labrador current Cold water travels down from the arctic.

At one point the two currents actually meet. The different densities means that just like air masses the two do not mix well! Instead of depressions being formed this ocean current junction is famous for its Whirlpools.