I recall reading that BA would allow cancellations or changes to telephone bookings free of charge within 24 hours. According to a report from the Air Transport Users Council BA also have a "24-hour rule as internal policy" for online reservations.
http://www.auc.org.uk/docs/306/An%20...s%20online.pdf
I've never tried doing this with BA but had no problem when I needed to change a restricted bmi ticket within 24 hours.