IMO year 11 is probably the best time to start WEX, so we'll done for being on the ball
quite a few places do take 16 year olds, your best bet is to research. Vets can vary on the age that they take people; small animal practices usually take 16 year olds, so ring them ASAP as they'll be getting booked up now for summer (plus you'll be competing with actual vet students on EMS & unfortunately they often take priority). Large animal can be funny; I was able to get into a mixed practice and see some farm work when I was 17 but a lot of people have said many won't accept under 18s due to insurance.
When I was 16 I used to volunteer at a Riding for The Disabled stable every Saturday and I thought that was a great placement
the staff were good at teaching and I loved working with the kids. I didn't learn or see any particularly technical 'vetty' stuff, but im not from a horsey or farming background so it helped my confidence working with bigger animals. I also volunteered at a petting zoo last summer which had lots of exotics, and they actually took volunteers from as young as 14!
I think ringing people for placements is much better than writing too, as they can give you an answer straight away over the phone.
The only thing I'd say is prioritise your grades over WEX & extra stuff; when I was in my first year of college I was trying to do volunteering, WEX, learn to drive, have music lessons & other extra curriculars and I basically failed AS chemistry and physics and had to do a third year. I don't regret doing the third year, because I got the grades I needed and it gave me chance to do more WEX & I was more mature, but there was a lot of uncertainty at the time. I did the old system of A levels but even then my college debated letting me resit a year and we didn't know if I'd even make it to the interview stage, let alone get offers. So remember: you only have two years to get the grades you need but you can take as many gap years as you need if you don't have enough WEX