There's disruption everywhere, whether it's the UK or abroad, and most of it is shortage of staff.
The media is the usual misleading claptrap.
EasyJet went from a 40ish% reduced winter schedule to their full 2019 schedule overnight. And they have neither the staff nor the aircraft to operate it. Also, their crews have little incentive to work, as they currently have no duty free or hot food to sell, coupled with a sickness policy that allows them a carte blanche sickness if they have 'covid symptoms', ie come back when you're feeling better.
In the meantime they're selling flights they couldn't possibly operate to keep the cash coming in.
From what I have seen on the front line at T5, we're operating a reduced timetable, for example, our afternoon flight to Newark yesterday (June 6th), was cancelled. In early MAY.

Short domestic flights do routinely get rearranged, but this is largely because there are legitimate alternatives to flying to Manchester/Edinburgh/Glasgow, and it is easier to combine flights and use a larger aircraft later in the day and use the three hour operational saving to keep another route on track/keep crews and aircraft in the right place for the start of the following day.
So, yes it's true that British Airways have cancelled flights, but the media reports give no context as what flying programme they are using as a reference, as we aren't selling a full timetable to begin with.
Most of our delays have been down to weather or ground delays due to congestion, which is as much because Terminal 4 is currently closed, as anything, although that will improve in due course as new staff get on boarded and the other airlines currently using T5 will be moving out.