US authorities introduced the measures, along with a ban on leaving seats in the hour before landing, after a man tried to ignite explosives as Northwest Airlines Flight 253 from Amsterdam approached Detroit on Friday.
He was overpowered by passengers before the device, understood to contain about 80g of high explosive, detonated.
It is alleged that Mr Abdulmutallab spent about 20 minutes in the toilet before trying to set off a device moulded around his body, which had apparently passed undetected through airport checks.
Transport Secretary Lord Adonis told the BBC the "enhanced search regimes" agreed with US authorities would lead to delays.
"I'm sure passengers will understand in the circumstances," he said, adding that Britain would consider ramping up airport security and having more in-flight air marshals.
UK airport operator BAA said airline staff were carrying out the checks and advised passengers to leave extra time to check in.
A British Airways spokesman apologised for any delays but added: "Safety and security are our top priorities and will not be compromised."
Those flying out on Saturday praised the airline for sending text messages warning of the new rules in advance.
Simon Calder, travel editor of the Independent, told the BBC about 25,000 people were leaving the UK on 100 daily US-bound flights.
"There's going to be more strain on the check-in desks, lots of people turning up at the airports don't know the new rule and of course there's lots of repacking," he said.
Mr Calder added that if the pat-downs were extended to all flights, it would get "very slow in terms of processing people".
Mr Abdulmutallab is said to have been an engineering student at University College London between 2005 and 2008.
But according to Whitehall sources he was denied a new visa this summer by the UK Border Agency after attempting to apply for a course at a bogus college.
The plane was carrying 278 passengers
The Metropolitan Police have been searching a flat at an apartment block where he is said to have lived in Mansfield Street, Marylebone, and other properties in the capital.
Officers have removed several items for examination, although the search is being scaled down as officers try to identify any of Mr Abdulmutallab's associates.
It has emerged that his father, a prominent Nigerian banker, flagged up to US authorities concerns about his son's extreme views.
The suspect may also have been on the radar of UK intelligence but did not cause American officials serious concern and so was not on the US no-fly list.
It is understood one of the British authorities' key priorities will be to check whether he has cropped up in the course of any other investigations.
In the US a federal judge has formally charged Mr Abdulmutallab with attempting to destroy the Airbus A330 on Christmas Day.
The hearing took place at the University of Michigan Medical Center where Mr Abdulmutallab is being treated for burns.
An affidavit filed in support of the charge stated: "As the flight was approaching Detroit Metropolitan Airport, Abdulmutallab set off the device, which resulted in a fire and what appears to have been an explosion."
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