You can apply to an organisation directly to work as a bodyguard or go through a recruitment agency specialising in security work. You'll need a Close Protection licence issued by the Security Industry Authority.
To get a licence, you'll usually need to complete the Level 3 Certificate for Working as a Close Protection Operative. This is available through training providers approved by the Security Industry Authority. Older qualifications may be acceptable, depending on when you got them.
Some employers may prefer you to have experience of working in the police or the armed forces.