You also need to be very realistic about what the job is. It isn't all saving the lives of people's cute pets.
Vets work in abattoirs, overseeing slaughter for example. It's a requirement to have a vet for certain things in the slaughter process.
Industrial farming can be brutal. Animals are discarded when no longer productive and their lives can be pretty unpleasant (although meeting legal requirements). Vets will work in and for industrial farming where animals are a commodity, and not an individual life
Plus - it's a private business. You won't have the resources to be saving any random stray left on your doorstep - vets needs to make a profit.
The pay is not brilliant - 25k on graduation and not great progression in earnings for many (you need to become a partner in a firm to earn big money) This might sound a lot if you are in a dead end job but you will have spent six years studying - you could do maths/computer science in three year degree and earn a lot more money in finance/programming/etc.
Pay progression much better for doctors for example.
So you could work towards it - but it would be a lot of work because despite all the bad sides I mentioned, lots of people want to do it!
So you would need to ace your A levels or Access to Uni course as well as get work experience.
But you need to be super realistic about what the job is.
Being a vet nurse is not "settling" and is more likely to be a role working with cats/dogs/horses and other pets. If the attraction of the job is working hands on with animals, vet nurses do most of that - they take care of them, feed them, nurse them, exercise them, calm them down etc, the vet swans in and does the surgery/prescribes the drug and then moves on to next patient.
Ongoing interaction with the animal is much less for a vet than a vet nurse.
You can look at apprenticeships to be a vet nurse which wouldn't necessarily require you to do a levels etc first or do an access to science course and go via the uni route.