Ah, now that's an interesting point I hadn't spotted before, EC261, Right to Care, clause 9.1:

Now this kicks in at just 2 hours on sectors under 1500 km, which from LHR is as far as WAW, FCO, MAD. LIS and NAP are further, so they are in the next band which is a 3 hour delay. The start of the delay clause says "When an operating air carrier reasonably expects a flight to be delayed beyond its scheduled time of departure..." and the various time bands follow. Because the Regs talk about "a flight" and "scheduled" it's not clear whether the clock starts at the time of the cancelled flight or the rebooked flight, but if the passenger turned up at the airport for the cancelled flight and was told there, then I'm fairly sure the 2 hours starts at that point, otherwise in the Twitter exchange it would be from the time of the new flight.

This isn't optional, the airline has to provide this whether it's fog, ATC or down to their own logistics. So once a shorthaul flight is delayed more than 2 hours, I think it would be reasonable for a passenger to select a few items and claim them back from BA. The exceptions would be (a) if a voucher was handed out before travel and (b) if the passenger was delayed in a lounge and had access to food and drink there. But if held at the gate, onboard or if the lounge only offered crisps and nuts - often the standard at smaller outstations - I think a pack of sarnies would be reasonable.

You can't expect the crew to do this (though the Regulation implies they should) but I can't see how BA could refuse a request for repayment, particularly if paid with Avios.