There was a similar situation around 10 years ago when the EU-US Open Skies agreement liberalised access to LHR for all US carriers. (previously only BA, VS, AA & UA were allowed to operate to the USA from LHR). The stateside carriers who were forced to operate from (mostly) LGW - at the time CO, DL, NW & US wasted no time in transferring their flights to LHR.Surely enough time for BRS to attract a long haul service and develop it enough so it sticks around once runway 3 opens.
Some have attributed CO's access to LHR as a contributory factor in the disappearance of CO 757s from BRS, and arguably BRS management can foresee history repeating itself once LHR is not so slot constrained, hence they are not pursuing the runway extension.
Interesting that of those four carriers which moved from LGW to LHR, only one now retains its identity! Arguably the spirit of Continental remains of course, thanks to the United livery, but a lot has happened in 10 years.