Well, you won't be able to do it for free, but if you want to pay for exam entry, tuition (or try and self study to save money, but you will probably need to pay for some resources e.g. textbooks), and for science subjects, the science endorsement...there's nothing to stop you from doing so.
It really seems entirely pointless though - what are you going to gain from a random A-level or GCSE that you can't or won't from your degree? If it's merely to explore an interest you'd be better off making use of your university's library resources to explore that area, and a single A-level or GCSE qualification usually doesn't mean much (the exceptions being GCSE Maths and English Language at grade C or above, which you probably will already have, and in that case you would be retaking rather than taking it as a new subject) to employers (or anyone else).