Private Candidates (A-Levels)

I have read about a level and gcse entry requirements, to the most prestigious universities in the UK. But I wanted to know, that do Cambridge or Imperial College of London accept private candidates?
My best friend asked me but I didn't know, so I thought to ask any of you guys, my best friend is going to do her A2 exams this upcoming year 2016-2017 but she realised at the wrong and late time that she wanted to do or change her a- levels. She is doing Maths, Psychology & English Lit but she wanted to do Chemistry. As she didn't pick chemistry at the start, it is too late for her now, so is it reasonable for her to take a gap year after finishing sixth form, and doing a chemistry a-level privately, as a private candidate?