You will need to do a degree in Paramedic Science. It does not have to be the full 3 year BSc, you can become qualified by doing a 2 year foundation degree, this allows you to become registered with the Health and Care Professions Council. You will need to have A-levels in science or a sufficient amount of science content in your degree, but you would to check this with the individual unis that offer paramedic science as to whether what you have is sufficient to meet their requirements.
You will need to fund this course yourself.
Here's a good place to start researching this career http://www.nhscareers.nhs.uk/explore-by-career/allied-health-professions/careers-in-the-allied-health-professions/paramedic/entry-and-training/
Hope this helps.