Hi!
It can be hard to find the right places to gain work experience, although it is important to have the right amount of animal handing experience. So is the quality of your reflection of the work you have done, you can sometimes gain important experience in other types of work.
Some universities are a bit more flexible with what can be considered as work experience. You could consider working in a kennels or cattery to show examples of animal handling. While working as a receptionist, barista or sales adviser would show great experience of a customer facing role. You could even show examples of team work through event planning, Duke of Edinburgh or theatre performance.
Hope this helps!
Bets of luck with your application!
Rebecca