As you have a BSc already you would not be eligible for Undergraduate funding in the UK due to Equivalent Level Qualification (ELQ) rules. So if you are able to self fund a second undergraduate degree, there is nothing to stop you applying. You will be asked to list all your previous studies, you will be considered as a mature student, so do not worry about your old grades too much. You will need to demonstrate an interest and ability in the subject you want to study now to convince the admissions tutor to offer you a place over someone else.
Contact the universities you want to study at directly, give a brief description of your study history and why you want study course X. Your recent graduation should help to demonstrate evidence of recent study.