BAA, which owns Heathrow Airport, made the following statement:
"Immigration waiting times during peak periods at Heathrow recently have been unacceptable and we have called on the Home Office to address the problem as a matter of urgency.
"There isn't a trade-off between strong border security and a good passenger experience - the Home Office should be delivering both."
Long queues had formed at passport control on Thursday and Friday.
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A lamp in the tower which houses Big Ben is to be switched off for the first time in more than 70 years.
Sir Bruce entertained audiences for more than seven decades.
Work in the tower will also pause over the bank holiday weekend.