Not during the 1970's, but during the 1980's, a quaint little west country airline called Brymon operated services to/from both LHR and LGW.
LHR services became on a codeshare with BA whilst the LGW services became under the "British Caledonian Commuter Services" brand, codeshares with both major players out of LHR and LGW.
If such has been done before then such can be done again except not out of LHR and perhaps not out of LGW, perhaps LTN for London and perhaps MAN for codeshare and/or other connections.