Pet shops? Petting farms? Usually lots of events including animals are looking for volunteers (although may not be directly related), but for example, the England agility dog team usually send out emails around my university requesting for volunteers during their training sessions or competitions. I've also been involved in running things like the Lincolnshire Show - again not directly including animals but it's an animal based environment. Other than that as far as I'm aware ZSL no longer offer work experience/volunteer positions and any zoo generally has a ridiculous waiting list - I applied for a 2015 position for Yorkshire Wildlife Park last year! The main source of my experience pre-college was from working in kennels as they're always eager for volunteers and then branched out to farm animals and exotics while at college.