A few weeks ago there was a similar story from the same company. They've been on Rogue Traders, and their (real) Trust Pilot reviews make interesting reading.
Dont see why BG should expect you to pay this rip off bill, I would refuse to pay it and let BG sort it, I mean not everyone would have that kind of money spare
There was a bloke on here a month or so ago saying that the plumber had claimed to replace a pump but clearly hadn't done the job... We told him to report it, but he wouldn't... That got charged to BG...