As of a few years ago BA operated a centre at Heathrow called EPIC - its underground somewhere in Heathrow and has all the computers, phones, faxes, emails etc to be up and running within a very short amount of time. I believe its manned by BA managers who are all on a duty list to be called up in the event of any accident/incident.
The centre also earns its keep by being "rented" out to other airlines and operators of public transport services to cover them incase of incident / accident, these companies pay a retainer to BA for its use if/when needed.
I had a tour some time a go and its a chilling place but quite obviously well set up to deal with relatives and media enquiries !
rt