Plus you have to prove to the UK government that you can 100% financially survive without a job (the student visa allows something like 20hrs a week employment) BEFORE YOU LEAVE THE COUNTRY. If you can't prove this, you'll get denied a visa and sad times all around as you will not be able to attend the school.
@historygeek, yes it is very hard to find funding for non-UK/Commonwealth/EU MAs. For funding, you would have to go into a MA/PhD and then go through the whole visa application process. The upside is that degrees are awarded in a faster timeline and are usually less expensive than US programs.