It might be harsh, but until you do some work experience (4 weeks is honestly not much and I would set it as a bare minimum) you don't know you want to be a vet, which is why it is required. There has been some changes to vet requirements recently as some unis do not stipulate a minimum anymore, but even then it is very heavily encouraged and if you do none it would be very hard going to get any offers - you are up against 10 applicants per place, and the vast majority will have the work experience. If a uni does stipulate a minimum, it is a requirement in the exact same right as grades - if you don't reach it, you will be instantly rejected so there is no point applying without. You can look up the individual uni requirements on their websites as they do vary. The entire application process will be based around your work experience, both the forms and interviews. If you can't get a good amount by the application deadline I honestly would very heavily consider taking a gap year to do more in and either apply (or reapply) the following year.
As above, it is hard to revise for SJT as it isn't necessarily a 'right or wrong' clear cut thing, it is to see your thought processes during scenarios and to see if your perspectives match their ideal candidate. You cannot really 'guess' what their ideal candidate is - each uni has their own visions for their students, which brings me to the next point that applying just to Nottingham may not be the greatest move if you really want to go into veterinary - it is extremely competitive and many applicants may not get any offers in their first application cycle even if they applied to 4 vet schools. Looking up topical vet affairs, ethical dilemmas and RCVS code of professional conduct etc may help you better gauge some of the scenarios the tests may present to you. Obviously I don't know your personal situation, but this is just food for thought before considering applying, I would definitely do a few weeks of work experience and a lot of research.