I wouldn't avoid Access as a mature student. Firstly, with Access you get yourself in education within a year (as opposed to two). Secondly, you are prepared for L3 education throughout the course. With A-Level, you're expected to come in with some recent educational experience. If you do a 1-year A-Level, you'd be really left behind and would have difficulty catching up.
Access is accepted by all unis in the UK. There is little difficulty with convertibility. You can get a loan for Access which will die once you start university. Expense should not be an issue.
As for the PS, it does not need to be fantastic to get an offer for law. For most law schools, the majority of applicants (i.e. 50%+) will get offers. Just make sure your PS is well-written, gets to the point, and focusses on law (and your capability/motivation) to study law and not irrelevancies like watching Suits and your dad being a notary.