At the moment they seem to be rebuilding the multi story carpark at terminal 1 and my favourite option of "long term short term" parkingisn't available (that's where they heavily discount the short term rate so you can just exit the terminal and go straight to where you left your car with no hanging around for valets and/ or buses.

If you want the avios, no reason not to book the BA offering, but if you choose valet parking, there are a lot of cheaper options available if you google on Parking at Heathrow!