I'm a first year vet student but I've just turned 25! I did my A levels as a mature student by finding a 16-19 college that accepted the occasional adult and completing my A levels just like everyone else, (but 6 years late). It's probably possibly to do access courses but I'd be really careful picking which one- certain vet schools only allow specific courses and not others, and dictate what scores you have to achieve throughout. I'd totally recommend A levels because studying for 2 years is the standard route and it gave me more time to organise work exp and prepare to apply in the 2nd year.
Don't rush a decision, find the right path for you, if you need to get a job and save some money for a few years then in my opinion you'd have a better shot at applying as a mature student as you can take the time to get a really good application. Plus then you've had general life exp, job exp, interview exp etc which will help you in vet school interviews.