Definitely worth getting some out of the way, you'll want a break during the summer before 3rd year starts rather than just doing placements for 12 weeks solid. Do you drive/how easy is it for you to travel to placements?
Dairy...
Fold Farm springs to mind as being easy to get to as it's just outside Barnet and definitely take AHEMS students as I've seen them about on visits to the farm. Think they do dairy for ice cream (or they did at least) and must have reasonable numbers based on their youngstock and the fact they've got themselves a rotary parlour. Other than that I can't think of any/many others off the top of my head, there's a fair few smallholders with some beef but even then they're unlikely to have enough stock to count as a placement anyway. Maybe consider going away? I went down to a farm in Somerset for a fortnight where they milked around 600, great fun, lovely area and people, loads of free booze and some cash at the end of it too. If you really want to stay close(ish) to London then Kent might not be a bad shout for dairy farms.
As for horses, just google riding schools in the area or something? Should be able to find places within London, Lee Valley for instance.
Pigs... maybe have to go further away.