From the BA website;
"What happens if I miss a connecting flight due to a delayed British Airways flight? What refund or reimbursement am I entitled to?
If a delay of five hours or more to a flight operated by British Airways disrupts a connecting journey for which you hold a through ticket (with a planned connection time of 24 hours or less) British Airways will offer to re-route you to your final destination. If you do not wish to travel, you can claim a refund of the parts of the journey not yet flown."
As has been stated previously, it depends on whether the tickets were purchased from BA as a through journey or whether they were purchased seperately.