Teen it depends on the airlines own policy.
Virgin is dual based. If you fly for them you will be based in both LGW and LHR. They get around the regulation by providing a special coach between the two (if you are regularly on the M25 between LHR and LGW you can see the big red Virgin coach with Dumbo the elephant on the side) as there is something written somewhere which says you can only be based at one airport.
BA is a slightly different story. The company use to have many bases around the UK but they are all more or less gone now with the exception of LGW and LHR. LGW was once split in two as Eurofleet and Worldwide. This all changes next month when it is merged. At present none of the EF crew could operate out of LHR however if the WW crew were needed to operate out of LHR because of crew shortages they could be bussed up. This will change next month and they will be unable to do so.
Likewise, LHR longhaul will be unable to cover shortfalls down in LGW when the onefleet comes into operation.
Hope this answers your question!