Not that familiar with UK versus here in US. Here we have community colleges and Vet centers and colleges all over.
My best advice is to GO TO THE SOURCE! If you can't get help online, then call, or better yet, GO visit tour local vet clinics and service centers.. ASK the Vet Techs there where and how they got their training. Ask a lot of people there from Vet DR.s on down to the secretaries, and DO NOT forget to check/visit your local Zoo as they will have some VERY highly trained doctors on staff with EXTREMELY wide experience in not just the everyday dogs and cats and birdies, but with the more challenging areas of exotic and wildlife husbandry and research.
And while we are on the subject, why limit yourself to Tech or Nursing duties? AT 22 you are perfectly set to go for a Doctorate of Veterinary Medicine and specializes in any are you want from domestic, to farming, to wildlife. That could easily become a VERY satisfying and EXCITING life. I went the other way and went into human medicine, If I had ir all to do over I think I'd have gone the veterinary route! Paths not taken!
separate Vet center? You are looking for a Vet college. There are only 28 Vet schools in the US. do a google search for them. You need a four year Bachelor degree before you can apply to any Vet school. They are highly competitive and extremely difficult to get accepted into. Have a Plan B set up in case you do not get in.- You will need top grades all through your undergrad studies.
In the US, very few students go to the same university for both their undergrad and graduate school studies. You are encouraged not to. So if you did your undergrad studies at OSU, you would want to look elsewhere for Vet school.