Not really (i.e. you can't wait at he gate for the next flight) as almost all gates (and certainly the ones BA use) have seperate arrivals and departures routes. There is a transit area off the luggage hall (when it's open) which brings you back upstairs but you'll still have to go through immigration if it's not (not generally a long process), exit, go to departures again, re-clear security etc.

It oculd be quick, but if the flight is on a tight turnaround, it might not work if you are delayed en-route.