The terror threat to the UK has been downgraded from "critical" to "severe".
BAA is still advising people not to bring hand luggage
Home Secretary John Reid said the change was made because an attack was "highly likely" but not "imminent".
The change in the threat level means the ban on taking hand luggage on to flights from the UK has been lifted, although some restrictions remain.
The BBC's Daniel Sandford says a handgun and a rifle have been found at two separate addresses searched by police investigating the alleged plot.
The change in the terror threat level was made by the Joint Terrorism Analysis Centre based on the latest intelligence.
The threat level was heightened last week amid fears of a possible plot to blow up transatlantic airliners. This prompted a number of arrests on Thursday.
Officers are continuing to question 23 people in the inquiry.
Mr Reid said although police believe the main suspects in the alleged plot had been arrested, there was still the threat of a terror attack.
Speaking at a press conference on Monday, the home secretary warned that "the change in the threat level does not mean that the threat has gone away".
He said: "The public needs to know that there may be other people out there who may be planning to attack against the United Kingdom."
Meanwhile, the US Department of Homeland Security has downgraded the threat level for flights from the UK from "code red" to "code orange".
The UK has been at the highest level of terror threat since police made arrests last Thursday in connection with the alleged plot to use liquid explosives on planes from the UK to the US.
Most airports around Britain, including Birmingham International, Belfast International, Cardiff International and Luton have now begun to implement the new hand luggage rules.
Airport operator BAA said the new rules on hand luggage, which will allow passengers to take certain items on board, should have come into force at five of its seven airports from noon on Monday.
Southampton, Stansted, Glasgow, Aberdeen and Edinburgh airports confirmed that they had implemented the changes.
But BAA said the relaxed rules would not be implemented at Heathrow and Gatwick until Tuesday.
But despite the security downgrading at least 24 scheduled flights between Scottish airports and London were cancelled on Monday. Most are British Airways services between Glasgow, Edinburgh and Aberdeen but easyjet flights have also been disrupted.
The Department for Transport said passengers would now be allowed to carry one item of hand luggage on to flights, although there would still be some restrictions in place.
The department hoped the change would help ease congestion at airports.
BAA chief executive Stephen Nelson said the current situation was "the biggest security crisis in aviation history in this country".
He also said he expected BAA's airports to be on "an improving trend" over the next two days and that extra staff had been brought in to help cope with the situation.
Searches of Heathrow's passengers have now been reduced to 50% from the 100% of passenger searches on Thursday.
Long-term changes to airport security checks outlined by Transport Secretary Douglas Alexander include the following:
Passengers can choose what to take on to a plane, but any form of liquid, fluid, lotion or gel will be banned. Electronic devices, such as laptops, will be permitted but will be thoroughly screened.
A medium-sized item of hand luggage will be permitted. This bag will be around half the size of luggage previously admitted.
Searches of passengers and their clothing will be conducted more frequently and are to be carried out by hand or using body scanners.
On Sunday night a British Airways flight was turned back after a mobile phone was heard ringing at the back of the plane and no one admitted to owning it.
Before the restrictions were changed, travellers had been told to expect more cancellations and delays at UK airports.
Meanwhile, detectives investigating the alleged plot are conducting a major search for evidence at King's Wood near High Wycombe in Buckinghamshire, near the scene of one of the raids.
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