BA does not have a kind of a 'stop in London for a few days' programme that some airlines do. Each fare will describe what you can and cannot do. Some fares do not allow stopovers at all; many fares require a payment but limit the number of days that you can stay in London; some fares require a payment and do not limit the duration of the stopover; and then there are fares that allow unlimited stopovers. But there is no universal policy or rule.