Something has gone wrong along the way - the £75 is a very reasonable fare, and as CWS says you are saving BA a hotel bill as well. Unfortunately, BA have a habit of nickel and diming its customers (and sister departments) and causing more trouble for itself in the long run.

A regular metered taxi to Whitechapel would be over £90, as a point of comparison. I'd be making sure now that I included the cost of getting back to the airport the next day, even if it was just petrol for a friend's car.