Package the meat in a polystyrene box with some freezer blocks, this should keep it cool for 24 hours. Use a local courier service for an overnight delivery, dropped off by 4pm is usually delivered by lunch time the next day. Make sure the box is well taped up. Cost is around £10 for upto 10kg.
If you go into your nearest wagon transport company they should be able to tell you who to use, these are much more cost effective than the main couriers, and they provide the same service.
Hope this helps.