Can I pay for an exam greater than A-level in the UK?
Speaking about education in the UK generally, the answer is probably no. The A-level exams correspond to qualification level 3, and anything above A-levels is considered higher education: bachelor degrees cover Levels 4-6, master degree is level 7, and doctorate is level 8. I do not know any HE provider in the UK awarding HE degrees by examination only. 

Having said that, the Open University provides many courses using distance learning, which do not require students to attend the campus, except for a couple of short periods each year.