The plane, bound for St Petersburg, crashed in Egypt's Sinai desert just 23 minutes after take-off from Sharm el-Sheikh on Saturday.
Most of those on board the plane, which was operated by Russian airline Kogalymavia, were Russian.
"We have concluded that there is a significant possibility that the crash was caused by an explosive device on board the aircraft," UK Foreign Secretary Philip Hammond told reporters after the government's crisis response committee met late on Wednesday.
He said Britain was suspending all flights to and from Sharm el-Sheikh indefinitely and UK nationals already there would be helped to leave once extra security measures were put in place.
The move came during a visit to Britain by Egyptian President Abdul Fattah al-Sisi and Mr Hammond stressed that the decision to suspend flights was made "very reluctantly", adding: "We have to put the safety and security of British nationals above all other considerations."
At the scene: Sarah Rainsford, BBC News, St Petersburg
Anxious for information, Olga Ovechkina and other relatives now come to a hotel near the airport each day.
It has become the headquarters for an emergency response team. Raw-eyed relatives wander the lobby here or sit quietly and cry.
Dozens of psychologists are on hand to offer comfort, themselves clearly drained by the experience.
Earlier, Prime Minister David Cameron's office said UK aviation experts had been sent to Sharm el-Sheikh to assess the security situation there.
Egyptian Foreign Minister Sameh Shoukry called the UK response premature and unwarranted, telling the BBC that Egypt had taken "exceptional measures" to enhance security at Sharm el-Sheikh airport.
Security concerns and the Sinai plane crash are expected to be high on the agenda when Mr Cameron and President Sisi hold talks on Thursday.
An unnamed US official told the Associated Press news agency they had reached the "tentative conclusion", after intercepting communications, that an IS affiliate in the Sinai peninsula had planted an explosive device on the plane.
"A bomb is a highly possible scenario," another US official told the AFP news agency.
But the officials stressed that forensic evidence, including the flight recorders, was still being analysed.
On Tuesday, US media reported that a military satellite had detected a "heat flash" over the Sinai at the time of the crash.
It said data was still being analysed and that although the flash could have been caused by a bomb, a fuel tank or engine explosion was also possible.
Mr Sisi, in a BBC interview on Tuesday, dismissed as "propaganda" claims that militants linked to IS brought down the aircraft.
The militants have carried out a series of deadly attacks against Egyptian security forces in recent years.
Kogalymavia earlier this week blamed "external influence" for the crash, but the head of Russia's aviation agency said such talk was premature.