The word soccer comes from an abbreviation of Association Football, which is the official name for the game. Association was abbreviated to assoc, which was shortened again to soc. And then in Rugby school they added the suffix -er: soccer. The suffix was adopted by Oxford University students and added to other shortened nouns. Rugger is probably the most common example, beside soccer. The Oxford English Dictionary also has brekker, for breakfast, bonner, for bonfire, and cupper, which was a series of intercollegiate matches played in competition for a cup.
And is it soccer, or football? The origins of soccer are decidedly British, and there are plenty of examples of soccer being used by British people over the years. But in terms of the history of the language, soccer is something of a Jonny-come-lately. By contrast, the word football has been around since the 1400s. Nowadays, to blend in with the diehard fans in Britain, it's better to stick with football.