Flights will probably not take off unless it's been confirmed that they can land at (or close to) their scheduled destination. So, for example, someone travelling back from Oz might be on a flight which refuels in Bahrain, resulting in the plane being held there until further notice.
Planes which were already in the air when UK airspace was closed were diverted to convenient airports. Many long-haul services were routed into Frankfurt, where they'll stay until they can continue their journeys. (Of course, it's not really as simple as that. Each plane will need a crew which hasn't exceeded their maximum working times, together with a departure slot which will have to be added into the schedule of one of the world's busiest airports).
Chris