Are you in your first year of A levels or the diploma?
For all the vet schools they ask that you have some experience working within a veterinary practice, also on farms as well. When would you be looking at applying? You would also need some work experience for the nursing degree, Nottingham Trent for example require applicants to have at least 2 weeks within a veterinary practice which has been completed within 18 months prior to applying.
The RSPCA are unlikely to take you on for work experience due to insurance reasons. A lot of vet practices (small animal) will take on under 18's, you just have to ask around - if none took students we wouldn't have any students accepted into vet school or onto vet nursing degrees. Most applicants to vet school have at least 2 weeks work experience within a veterinary practice, alongside placements on farms such as lambing, dairy, beef or pigs.
Where in the UK are you?
Work experience wise try kennels/catteries, go into as many small animal practices and ask in person if you can do some work experience, tell them why you want to do the work experience, you need to get out and do this in person, rather than just ringing up or writing a letter. When I worked as a vet nurse I preferred work experience students to come in and ask, rather than contact via phone/letter or email (I arranged all our placements for the practice). For farm placements if you do wish to do veterinary, Google local farms and visit them, ask if you can help out in mornings/evenings. You need to be willing to work hard, and be enthusiastic about it.
Both veterinary nursing and veterinary medicine are challenging careers which require a lot of dedication, to get on to either course you need to show that you know what's involved and show that you've experienced life within a practice.
If you work at it, you'll get the experience but you've got to put the effort in to get the placements to get there - don't worry!
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