[ajb]

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.

[fredoralive]

The Piccadilly line isn't noted as suspended, presumably it has its own electricity feed, so there are even still trains you could get.

[gambiting]

Also it's not like Heathrow is on an island, in the worst case you could get everyone out by buses.