That current (called the Gulf Stream) is coming from the Gulf of Mexico (hence its name), which is tropical and warm. England gets a warmer climate because of the tropical warmth coming from this current.

I read today that the current you were talking about, the Gulf Stream, transports more water than all the rivers in the world combined. It splits from the East coast around Cape Hateras and then moves eastward like you said.

Right now there are several competing hypotheses about whether the current causes Europe to warm or not. According to one that has been popular for a long time, the Gulf Stream brings warm water to Western Europe and heats up the coast there. This might happen because the water causes changes in which direction air flows from. According to the other hypothesis, the changes in air are just caused by mountain belts. Because the Rocky Mountains divert air flow in different ways, the East coast is colder than Western Europe.

Most scientists agree that the wind directions cause the actual warming, but how those winds are influenced by ocean currents is still up for debate.