The joint BA/BCal Airlink service operated between LHR and LGW from 1978 to 1986, with the S-61N G-LINK actually being owned by the BAA. It ceased shortly after the M25 link between the two airports was completed.
I only flew it once, I seem to recall that it departed from an area adjacent to where the cargo tunnel emerges in the Central Area at LHR, but I don't recall where it terminated at LGW.
Interesting article on it here:
Gatwick/Heathrow Airlink 1978-1986 | A collection of articles from a 36 year career in aviation.