Most of the British holidaymakers stranded in Sharm el-Sheikh who had been due to return to the UK by today will be home by the end of the day, Transport Secretary Patrick McLoughlin has said.
Airlines will resume services from the Egyptian resort amid tightened security, including a ban on carrying hold luggage.
The UK government suspended air links on Wednesday after a Russian plane crashed last weekend, killing 224 people.
It has been reported that British spies uncovered an Islamic State (IS) bomb plot in the region following the tragedy.
Prime Minister David Cameron said it was "more likely than not" the Russian aircraft was brought down by a terrorist explosive device.
The Government gave approval for flights to resume after a day of intense negotiations with Egyptian leaders and the airlines.
Mr McLoughlin told ITV1's Good Morning Britain: "The airlines have been incredibly co-operative with us to sort this out and we are going to have a number of aircraft going out today and bringing people back home.
"I think most of the people who were expecting to be home by tonight will be home by tonight."
Mr McLoughlin confirmed that British experts had visited Sharm el-Sheikh airport 10 months ago to check on security arrangements and had "satisfied ourselves that things were OK".
Asked on Good Morning Britain why security failings had been missed, the Transport Secretary said: "I don't think we missed them. We took a view on security as we saw it on the day.
"Things have moved on, and what happened on Saturday and the subsequent information we got gave us very great concern indeed about the security, and that's why we took the decision that we took.
"We have to work with the authorities in these airports and we got assurances that things were improved. Obviously, things have changed."
Mr McLoughlin said the UK routinely sent experts to airports around the world to check on security, and said this week's events would "send a message" to other countries about the need to maintain standards.
But he said it was not possible for Britain to intervene and provide its own security if it was concerned about measures in place: "It's absolutely right that it has to be the state involved that does security. We don't have the power."
The Transport Secretary said the Egyptian authorities had been supportive in satisfying British concerns over security. He confirmed that the UK had received "evidence that it could well have been a bomb" that brought down the Russian Metrojet Airbus A321, but added: "We are wanting to see the inquiry come to fruition."
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.
Announcing the resumption of flights from the popular Red Sea beach resort, Downing Street said: "Our utmost priority is to make sure we have all the right measures in place to ensure that British citizens can return safely to the UK.
"The Prime Minister held talks on the situation with President (Abdel Fatah) Sisi and, following further discussions with the airlines and the Egyptians, we have agreed on a package of additional security measures that is being put in place rapidly.
"The additional security measures will include permitting passengers to carry hand baggage only and transporting hold luggage separately."
Outbound flights from the UK to Sharm el-Sheikh remain suspended and the Foreign Office continues to advise against all but essential travel by air to or from the airport, but the UK is continuing to work with Egypt to get back to normal service "as soon as possible", said Number 10.
EasyJet, Thomson Airways, British Airways, Thomas Cook and Monarch all announced they will operate to the UK on Friday, including a number of "rescue flights".
Mr McLoughlin said hold luggage was "one of the big concerns" about security. The restrictions mean that anything that cannot be taken into the aircraft cabin will have to be transported back to the UK separately.
The Association of British Travel Agents (Abta) advised holidaymakers to contact their airlines about travel arrangements.
"As a result of the current situation, holidaymakers travelling from Sharm el-Sheikh airport will have to follow certain special procedures as set out by the Government, including restrictions on taking hold luggage and the size of hand luggage," a spokesman said.
"Whilst it is appreciated this may cause some inconvenience, these procedures are being implemented for the security and safety of passengers and it is important that passengers follow their airline's requirements."
Mr McLouglin declined to comment on the credibility of claims by Islamic State militants in the Sinai Peninsula that they were responsible for bringing down the Russian plane.
But the BBC reported that UK security agencies had received intelligence on Wednesday based on intercepted communications between Sinai militants which pointed towards a bomb on the plane.
They were reported to suspect that an explosive device could have been placed inside or on top of luggage by someone with access to the hold just before take-off.
Although British officials have not ruled out the possibility of a technical fault, they think it is increasingly unlikely, the BBC said.
Mr McLoughlin said that "well in excess of 20" flights would be leaving Sharm el-Sheikh with British holidaymakers on board over the course of Friday.
Around 15 flights scheduled for the major changeover day of Thursday were cancelled because of the security concerns, he said.
The Transport Secretary told BBC1's Breakfast: "This has been a very difficult set of circumstances and I do understand the frustration felt by people who are on holiday wanting to return home."
He said current restrictions on hold luggage and the suspension of passenger flights intoSharm el-Sheikh would remain in place "until we've got longer-term assurances about the security at the airport".
He added: "At the moment, the advice is that we don't advise people to fly into Sharm el-Sheikh. We don't have any problems with the safety of the resort itself but we are concerned about flights into Sharm el-Sheikh.
"I hope we can restore our confidence in the security of the airport as soon as possible."
Mr McLoughlin said that a bomb in the hold of the Metrojet plane was "a high probability".
He told Sky News: "We've made our position very clear on that, that we think that is a high probability. We are obviously waiting for final confirmation of that, but we felt it was right to act on the information that we got and we did act."
Mr McLoughlin warned the flight ban could be extended to other countries if security was found to be lax.
"What this makes clear - not just to the Egyptians but to other airports around the world: if we are concerned about their security we will not hesitate in taking the kind of action we have taken this week for the safety of British passengers," he told BBC Radio 4's Today programme.
He denied British security officials were powerless to prevent abuses because they had no control over screening staff.
"We can make it as difficult as possible," he said.
"We are not recruiting those people, that is absolutely true - but we can express to the governments, to the airport authorities what procedures we expect them to go through.
"If we are unhappy with the way it is implemented, we won't hesitate to take the action we've taken."
He said he hoped to get the hold baggage back to passengers "within the next week to 10 days" but did not expect it to be transported by the RAF.