No way! That back tyre was new when you got the bike!
I paid £111 for a new BT020 but they vary from upto about £130.
The guy that fits my tyres comes to you, excellent service and a nice bloke too. Call G&S Tyres on 01189 629561 or 07702 391071.
Hope you get it sorted.
Dan
Edit: And in the same situation I would have called Stuart as he has a trailer and lives in Sandhurst!