Employers will be more interested in your technical skills and practical experience than your formal qualifications.
In practice, many camera operators take a college or university course to develop the necessary skills before looking for work. Relevant courses include: City & Guilds Diploma in Media Techniques (7501); BTEC National Certificate or Diploma in Media Production; BTEC HNC/HND in Media (Moving Image)
degrees in media production, media technology or photography. The most useful courses offer practical experience and may include work placements - check with colleges or universities for exact entry requirements.
As well as gaining technical skills, you should also build practical experience and make contacts in the industry.
Courses can help you with this, but you can also get useful experience from: getting involved in community film projects; working for a camera equipment hire company; finding work experience as a runner or camera assistant with a production company.
You may also find it useful to have skills in stills photography and basic electronics.
You should also make a 'showreel' DVD of productions that you have worked on, to demonstrate your skills to employers when you are looking for work.