A spokeswoman for BAA, which owns Heathrow, said Friday night's long queues, which saw passengers waiting for up to an hour, had cleared by midnight.
Discussing the situation today, she said:
"Everything is looking quite good in the immigration halls. Things are moving and we haven't got major queues.
"The Border Force is putting staff where they are needed at the moment."
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RMT members staged a protest outside Parliament to mark the anniversary of the first strike one year ago today.
The former mayor of Tower Hamlets, was forced to step down after he was found guilty of a string of corrupt and illegal practices.
The service is the first to be held in the singer's honour since the private funeral held by the family at Highgate Cemetery on March 29.