It is best to do a course to learn the art of makeup. The London College of Fashion seems to be the best course available according to professional artists.
There are also private courses i.e. Greasepaint, Brushstroke and London Esthetique but these are shorter courses and very expensive, they offer an agency service too but it is not to be relied upon.
After training it is a good idea to assist established make-up artists and perhaps even do a few unpaid short films to gain experience and fill up your CV.
It's a very competitive industry to get into so you need a lot of determination!
For questions around this and other creative jobs, the Arts Council of England has a site called 'Your Creative Future' with good links and advice.