From memory, it hasn't been proven that badgers are the cause of the tB. Some theories hold that the badgers do transmit it, but that they pick it up from other cows first.
As for culling, all that does is, as already noted, increase the movement of the badgers, thus increasing the likelihood of badger/bovine interaction. Where culling does work is in areas where the badgers cannot move into the recently culled areas. A study was done in Ireland on cattle farms that were bordered on several sides by impassable terrain (busy roads, rivers, cliffs), on any other sides a further area was culled and monitored to create an artificial barrier. On these farms cases of bovine tB were reduced.
This won't work in the UK though, as we have few places that match the isolation required.
They are protected by law, but licences can be granted to cull or move them where all other options have been tried and failed.