So there's actually two answers to this question. The Gulf Stream is part of the reason why Britain is warmer, since it carries so much warm water, but the difference between a maritime and a continental climate is more important. At the latitudes of Canada and Britain, the prevailing winds are coming from the west. If you're in the east, the prevailing winds are gonna have to travel all the way across the ocean, which will lead to it being warmer in the winter, and colder in the summer. If you've got thousands of miles of continent out to windward, your climate will be more extreme. If you're going across the entire ocean, it's gonna be more mild, and predictable. Continents just get hotter and colder than oceans, and this affects the temperature of the atmosphere passing over them.
