Can I pay for an exam greater than A-level in the UK? I know that in the United Kingdom I can sit examinations equivalent to GCSE/A-levels without actually doing the years required in a school or other institution.

I want to know if there are other exams that I can sit that are considered higher than A-levels and I am given a certified certificate of qualification, without spending time in any institution, all that is necessary is to arrange payment for this exam at a centre. And if I pass then I receive the qualification.
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.