You can get the same type of service from
Purple Parking, who I've been using for years, for significantly less. They collect the car from you outside the terminal building, and deliver it back to you at the same place when you return. They are charging about £35 return (or £17.50 each way, if you only need the valet service on way) in addition to the car parking which is about £7 per day. For a two day weekend, that BA service wants about £66, compared to £49 for PP.
The BA service at T1 is also
ceasing from 26 October 2003.