Passengers are still waiting for their transatlantic flights
All US airspace has been closed since Tuesday afternoon, and all flights from the UK to the US and Canada remain suspended.
Flights over central London have been banned.
Tightened security is in place at airports across the country.
The Association of British Travel Agents (ABTA) said anyone hoping to go to the US before Friday should assume their trip had been cancelled.
Anyone heading to New York, Washington or Boston airports within the next week should also consider their trip cancelled.
All passengers are advised to check with their airline before departing for the airport.
Thousands of UK holidaymakers - 14,000 were due to fly to the US on Wednesday from Gatwick alone - remain trapped at airports.
Trapped at Heathrow
At Heathrow many passengers faced another night on Wednesday at the airport or a search for a hotel room.
Most passengers seemed resigned to the disruption but some said airlines had coped poorly with the situation.
Nathan Thorne, 28, who was heading to the US, said: "There was an 82-year-old lady getting her ticket re-issued in front of me.
"She was travelling alone and the airline couldn't even offer her any help, just told her where the bus station was. For me, it is probably not that big a deal but for an 82-year-old lady it is pretty bad," he said.
On Wednesday most airports were reporting that non-transatlantic flights were running with only minor delays.
But London City Airport has cancelled all inbound and outbound flights until at least midnight.
A government security meeting put a no-fly zone above central London.
London no-fly zone
The RAF is reported to be on standby to shoot down any aircraft which ventures into the zone.
Security measures have been stepped up across the country and airports were advising passengers to allow plenty of check-in time.
The extra security measures were so time-consuming that low-cost UK carrier easyJet cancelled a number of European flights.
Police at Heathrow reminded people travelling abroad not to carry knives on their person or in their baggage.
The Foreign Office is advising international holidaymakers to keep a low profile, amid fears of attacks because of the close relationship between the UK and US.
Holiday refunds
ABTA spokesman Sean Tipton said it was safe to assume all US-based holidays would be cancelled on Wednesday and Thursday.
"But don't assume trips after that will be cancelled, because if you don't turn up you probably won't get your money back," he warned.
Passengers should ring their travel agent or airline to find out the state of play, he said.
But Mr Tipton said that as the circumstances were out of the control of either the airlines or the tour operators, no compensation was likely to be given.
Package holidaymakers in the US due to fly home on Wednesday or Thursday were advised to contact their local representative for updates.
Independent travellers should get in touch with their insurance company and their airline.