The easyJet plane has taken off from the Red Sea resort, and UK ambassador John Casson insisted more will leave during the course of the day.
The departure came after the airline released a statement confirming that two flights would be leaving, but claiming the airport authorities had suspended permission for another eight.
However, other carriers suggested they were still expecting to operate flights back to Britain.
Speaking to reporters at Sharm el-Sheikh airport, Mr Casson denied the local authorities were blocking flights.
“We have very good cooperation. The first two flights are leaving now as I said, there will be more flights during the day, and we will continue to work until we have everybody home,” he said.
“There are challenging logistical difficulties to work through, this is a busy airport, and we need to make sure people leave in a way that’s safe and is in line with international aviation regulation, and that’s what we’re doing and we’ve got very good progress in our collaboration with the Egyptians.”
In an apparent indication of frustration with easyJet, Downing Street said it was important for airlines to give tourists “accurate information”.
“I think it is important that all the airline companies work closely with us to ensure that what they are telling customers is accurate and that they are giving them the best possible information,” a Number 10 spokesman said.
One element in hold-ups at Sharm is the presence of a broken-down aeroplane, which was causing an issue in terms of getting flights in and out, he said.
Some planes have been in Sharm el-Sheikh since being grounded on Wednesday, while others are being flown empty to the resort from the UK.
Egypt’s civil aviation ministry denied that they were to blame for delays.
A 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.”
The UK Government suspended air links on Wednesday after an Airbus 321 operated by Russian airline Metrojet crashed on Saturday, killing 224 people. Militants of the Islamic State terror group in the Sinai Peninsula have claimed that they downed the plane.
Transport Secretary Patrick McLoughlin said information obtained by UK officials indicated there was a “high probability” that the plane was brought down by an explosive device, though he said he was still waiting for final confirmation.
There have been reports that security agencies received intelligence based on intercepted communications between Sinai militants which pointed towards a bomb on the plane. They apparently suspect an explosive device could have been placed inside or on top of luggage by someone with access to the hold just before take-off.
Tourists arriving at Sharm el-Sheikh airport for flights scheduled for 11am Egyptian time were met with chaotic scenes.
Would-be passengers who had checked in were left sitting in departure lounges with the planes visible on the tarmac outside. Others said they had been sent back through security and told to return to their hotels.
Mr Casson was heckled by angry holidaymakers as he walked through the airport, with one woman repeatedly demanding: “What’s the problem?”
Another asked: “When are we going home?”
The ambassador insisted the “aim is to get as many people home as soon as possible”.
Asked if he was satisfied with the level of security at Sharm el-Sheikh after emergency measures were put in place, Mr Casson said: “Yeah. We would not be allowing flights to go back to the UK if it weren’t for the fact that we have the additional package of security measures in place to allow us to let people fly home safely.”
The UK’s decision to reveal its belief that terrorists may be to blame has angered both Moscow and Cairo.
President Vladimir Putin told David Cameron in a phone call on Thursday that all countries should wait for the completion of the Russian-Egyptian investigation before reaching conclusions on the cause of the crash. And Egypt’s foreign minister Sameh Shoukry said he was “surprised” by the UK’s “somewhat premature” decision to suspend flights.
The Government gave approval for flights to resume late last night after a day of intense negotiations with Egyptian leaders and the airlines, including face-to-face talks between David Cameron and Egyptian president Abdel Fatah al-Sisi, who was on a pre-planned visit to Downing Street.