It may do. From a time perspective, you could argue the time taken to fly LBA-LHR (1hr?) but then all the waiting in queue, then transferring into London makes it look pointless.
However from a connectivity perspective, people would still use the flights to connect onto onward destinations, much less hassle than lugging all your luggage onto a train, where you may/may not have space for it, onlt to then transfer further toawrds LHR/LGW.
End of the day, the demand will still be there