BT's warning message advises customers to contact customer services if they want the block on the site to be lifted.
Are BT just trying to get loads of complaints, so they prove they tried to stop piracy and discovered it wasn't commercially viable? Either way, I'd recommend calling up and complaining, even if it means waiting on hold for an hour. Threaten to change your service provider. Enough people do that, I'm sure they'll sit up and listen.
Happiness is a positive cash flow.