The substations decribed in the power network case study above are for local distribution – 33kV stepping down to 11kV (×2) and 11kV to 415V (x12).
The substation on fire (North Hyde) is a 275kV major distribution substation.
That's a fairly significant distribution loss in itself (not just Heathrow but also 16,000 homes), and rebalancing the distribution will need careful coordination – flipping the switch on a load the size of Heathrow would then imbalance the network for the new distribution supply site.
Speak for yourself, if mine don't bring in £50 a week each from their car-wash, it's 3 days in the cell in the basement on bread and water. For all of them. They're learning the importance of contributing.
UK Power Networks are the local network operator for London and the South East. The substation that has gone boom is a National Grid one, so it's presumably affecting things upstream of local substations. I'm surprised there's a single point of failure at this level though, you'd think Heathrow would be considered important enough to have multiple feeds at a national grid level.
Literally just guessing: that substation is on the train route to central London, which is the main public transport connection in and out of Heathrow. Indeed the Elizabeth tube line is suspended on the Heathrow branch.
So perhaps the core issue isn't inability of the airport to operate, but of people to get in and out.
I think it's likely the Elizabeth Line branch is suspended because the stations are closed, and the stations are closed because there's no power to the buildings.
Other trains are running on the main line through the area. It's 25kV electrification, there's plenty of distance between feeder substations.
National Rail say [1] "An unadvertised shuttle service is running from Heathrow Terminals to London Paddington to ensure customers and colleagues can leave the airport" so trains can and are running, they just don't want flight passengers to go to the airport.
I doubt they would suspend flights for that. Heathrow is used by people from all over South England, not just London, so a good proportion of customers come by car. Not to mention the people doing transits. Also TFL has a stock of buses which they use if a rail line goes down.
Sounds weird that one substation going down would close everything.