A quick delve through the archive in the garage which covers mid 1970s to mid 1990s:
Gatwick services started in 1979 with a BCal Piper Navajo Chieftain 3 x daily, originating in LGW
By Summer 1980 this was a Brymon Twin Otter running 3 x daily and doing a PLH-BHX early morning and BHX-PLH late evening
Summer 1981 this was a Brymon Twin Otter running 4 x daily and based at BHX by then
This looks to run right through to 1990 when a Brymon Shorts 330 (must have been leased?) is showing 3 x daily BHX-LGW services
Service disappeared at the end of Winter 1990/91
Heathrow services were running on a mix of aircraft with British Midland normally at 5 x daily frequency - Viscount in 1980, F27 by 1982, Shorts 360 by 1985 and then ATP from 1989 until 1992. A Dash Seven then flew the route in 1992 and 1993 (aircraft in the fleet after the EuroCity Express experiment at LCY) and British Midland services then stopped at the end of Summer 1993.
Community Express had a short-lived attempt to fly EMA-BHX-LGW with a Shorts 360 in 1996.
Apart from positioning flights, those are the last regular commercial services on BHX-LON I can see. Happy to stand correct - and I'm sure there's much history before that time - if anyone has further info.