Well, according to ba.com, we were both wrong (though you were more right, TBS )

http://www.britishairways.com/travel...public/en_gb#U

Weekdays, 8am to 8pm.
Weekends, 9am to 5pm.

Though I guess it may be open longer now during the disruption. Mind you, I don't believe ba.com - I've called at 6am UK time when I thought it opened before and got through as recently as a few months ago.

Edit: Ah, AskBA explains it all So it's open from 06:00 weekdays, but 'queries and assistance' are only available from 8am. Nice

To the OP - there are some numbers on that link if you want to try them, though as I say, I normally just do the +44 on the freephone I'm sure.