Providing transport to the other airport is a requirement in the EU261 legislation, whether the delay is within the airline's control or not, unless you opt for a later flight voluntarily. My understanding is that
BA» 's standard policy is to refund the reasonable cost of reaching the alternative airport (i.e. the tube/
DLR▸ fare on a normal day, or a taxi where there is no public transport).
The EU261 regulations also require re-routing, regardless of delay cause. In practice, you'll only be booked on an alternative carrier if there are no flights on the same or next day. And then you'll likely only be offered a oneworld flight (in the case of BA). Even the likes of Ryanair, although not part of an alliance, will only book on certain airlines (easyJet, Jet2, Vueling, CityJet, Aer Lingus, Norwegian and Eurowings, for reference).
You actually get a lot more rights as an air traveller (on journeys covered by EU261) than a rail passenger. Things like food and drink, telephone calls, hotels and transport are all a legal right, regardless of the cause of delay.
Paying for hold baggage has made the cabin baggage overcrowded so you are likely to get picked off and asked to put you baggage in the hold (for free). Annoying when you hadn't planned on it.
Experience suggests BA will allow hand baggage to be checked in before security free of charge (not advertised). They even have a "hand bag drop" desk at LHR T5, you just have to know about it to realise what it's for