So stop listening...
Easy answer here, stop listening at all to BBC content.
There is nothing the BBC broadcast on radio which does not have an alternate equivalent on TuneIn. When the BBC see their listening numbers are dramatically falling (online) they will realise the error of their ways. This is a blatant attempt to bolster a new content service they are offering to justify the expense of developing it at the tv license payer's expense.
Oh and write to your MP complaining about this... The BBC is doing less and less to justify the license fee "tax" and ultimately the only thing they will respond to is the threat of losing license fee money.