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David Cameron has said he is working closely with Egyptian authorities to get Brits out of Sharm el-Sheikh "as quickly and safely as possible".
More than 20 UK-bound flights were scheduled to leave Egypt today but some flights have been halted.
British tourists have been pictured boarding an easyJet plane in Sharm el-Sheikh.
It follows confusion over whether the airline's planes would be able to depart the airport for the UK today.
A spoksperson for the airline said: "The situation for UK flights in Sharm el Sheikh remains fluid. We are being advised that the Egyptian authorities will allow a restricted number of UK flights from Sharm el Sheikh today, two of which are easyJet flights."
The UK's Department for Transport has confirmed it is "working with the Egyptian authorities to try to ensure planned flights leave" Sharm el-Sheikh today.
A spokesman for the government department said: "We are urgently working with the Egyptian authorities to try to ensure planned flights leave Sharm today.
"Travellers should keep in contact with their tour operators and shouldn't leave for the airport until they have a confirmed flight. We ask for people's patience at this difficult time."
Officials from both Thomson and British Airways have confirmed their planned flights out of Sharm el-Sheikh back to the UK will be "continuing as planned".
A Thomson spokesman said: "All Thomson flights out of Sharm el-Sheikh are continuing as planned."
A spokeswoman for BA said: "Our one flight from Sharm later this afternoon is due to depart for Gatwick as planned."
The Egyptian civil aviation ministry has denied that it is "blocking UK planes' from arriving at Sharm el-Sheikh airport and said flights were "limited by airport capacity".
A ministry spokesman told Reuters: "Flying out thousands of people on one day is incredibly hard. Everyone has to go through the procedures.
"We have not cancelled any flights but the airport cannot handle all these planes at once."
One of the easyJet planes due to fly Brits stranded in Sharm el-Sheikh is seemingly being unloaded on the runway.
ITV News Correspondent Dan Rivers tweeted this picture from the airport saying it was a "confusing situation".
It comes after rescue flights sent to bring Brits home were "suspended by Egyptian authorities".
Monarch airlines has confirmed it currently has flights heading to Sharm el-Sheikh airport to bring stranded British tourists home and said it expects "all our aircraft to depart as planned later today".
Monarch officials said: "As far as we are aware all five of our planes are going to take off as scheduled and we have not heard anything to change that from the Egyptian authorities."
It follows reports from easyJet that Egyptian authorities had 'suspended' it sending extra flights in to collect passengers.
Crowds of British tourists continue to be stranded at Sharm el-Sheikh airport as they await news following reports that Egyptian authorities have suspended UK rescue flights entering the airport.
Egyptian authorities have reportedly 'suspended' extra flights headed to the country's Sharm el-Sheikh airport, meaning planes being sent out to bring stranded British tourists home are unable to continue as planned.
EasyJet posted on its website : "Unfortunately the situation in Sharm El Sheikh is very unclear. Our rescue plans that were put in place yesterday have been suspended by the Egyptian authorities.
"Discussions are currently on-going at the highest political level to unblock this situation. We are very sorry and understand that this is extremely frustrating for you – unfortunately the situation is outside of easyJet’s control."
The first two planes bringing British tourists home to the UK had already set off from Sharm el-Sheikh before the new restrictions were put in place.
In total 24 flights had been planned for today, 10 operated by easyJet, nine operated by Thomson and five operated by Monarch.
Families are among those waiting at Sharm el-Sheikh airport to board some of the first flights home to the UK.
It follows the lifting of a suspension put in place by the UK government amid fears a bomb may have been behind the downing of a Russian passenger jet last week.
The Stevenson family told ITV News correspondent Dan Rivers they were waiting for a flight to get them home to Brighton.
Latest ITV News reports
Monarch has cancelled all flights to and from Sharm until December 19 as the Government said direct returns would end after November 17.
New mum who was stranded in Sharm el-Sheikh says "words can't describe how happy" she is to be reunited with baby after return from Egypt.