Why not ask (one of)the City Farm(s) nearby? Or London Zoo. They have animals, so I suspect they get bales in. You could probably get a reasonble deal by riding on the back of whatever arrangements they may have, and if you wanted to make them a donation as well, then that's your business. There's a City Farm in Surrey Quays (and I think there's one in Lambeth, and also one over Docklands-way, and/or Hackney)
I imagine it's not really cost effective for anyone to bring in bales to Central London for a one-off venture, but there are farms in quite nearby places (I've been to one just out beyond Blackheath), so a phone book search for farmers might also work.