Hey,
It depends what you got in your A level results (Pm me if you want)
You can do an animal science/biovet/biology degree if you like, and it would get you on track to becoming a vet, BUT you would have to get a 2:1 or above in the degree after the three years, and I know Liverpool for example require you to have the following (you will have to check with the other universities)
Bioveterinary science, zoology or animal science degrees; grades CC in biology and chemistry at A level
Science (BSc) degrees, grades BB in biology and chemistry at A level
Arts (BA) degrees, grades AA in Biology and Chemistry at A-level
Other universities may differ when it comes to what A level they require with the degree, but use Liverpool as a guideline.
You'll be classed as a graduate applicant, so you will be viewed differently to A level students, but you will also be up against a lot of other graduate applicants when it comes to applying, so you must have the relevent grades which they ask for, and keep your work experience up to date.
I'm a current graduate vet student, if you have any other questions Pm me and I'm happy to answer them as best as I can