Remember that many employers accept applications from graduates with any degree subject, so don't restrict your thinking to the jobs listed here.
Many organisations working with animals in the UK are charities, so they rely heavily on volunteers. This is great news in terms of gaining work experience. Approach animal sanctuaries, rescue centres, visitor attractions with animals on site, zoos, safari parks or veterinary practices to offer help. Often organisations have volunteering sections on their websites.
You may be able to find work on livestock farms, particularly during seasonal peaks, such as when animals are birthing. You could volunteer as a dog walker for elderly people unable to exercise their pets, or write campaign documents for animal rights organisations. If you don't have much time to give, you could help out at animal events such as horse shows.
For those with a thirst for adventure, there are opportunities for animal-based gap year experiences, holidays and welfare projects. Some of these will be on a voluntary basis, and others will have cost implications.