Passengers said it was "chaotic", with huge crowds snaking around corridors and a lack of senior staff.
Airport operator BAA said UK Border Agency's service was "completely unacceptable" but queues were easing.
The agency blamed the Easter holiday for the length of the queues.
BAA said queues began easing after 13:00 BST with passengers in Terminal 5 having to wait the longest - 31 minutes for EU passengers and 51 minutes for Non-EU citizens.
The shortest waiting time was in Terminal 4, where it took four minutes for passengers from the EU to clear the checks and two minutes for non-EU nationals.
BAA said on Friday the longest wait passengers had was 77 minutes at Terminal 3, 75 minutes at Terminal 4, and 54 minutes at Terminals 5 and 1, with non-EU passengers facing the longest wait at the time.
Matthew Donaldson, 38, from Lincolnshire, who arrived on a flight from Cape Town in South Africa at about 06:30, said he had to wait for an hour and 45 minutes to leave passport control at Terminal 5.
He said: "It was complete chaos. Half the escalators were closed to slow down the crowds and when we got to passport control there were snaking queues.
"They gave no reason and there were no senior staff there.
"It was erratic to say the least."
George Galanopoulos, founder of London Executive Aviation which runs private jets, wrote on Twitter: "Just landed at Heathrow T5... total chaos! Embarrassing for London."
Simon Baugh, director of media relations at BAA, said the earlier situation at passport control, which is managed by the UK Border Force, the section of the UK Border Agency in charge of entry to the UK, was "fairly typical" but "completely unacceptable".
He said: "It's the UK's reputation and BAA's that suffers. There's no need for it.
"It's entirely about the level of resourcing the government needs to put in place."
A UK Border Agency spokeswoman said: "We will not compromise border security but we always aim to keep disruption to a minimum by using our staff flexibly to meet demand."
She said there were extra workers at the border over the Easter period.
Culture Select Committee chairman John Whittingdale outlined his committee's concerns about the airport's service in a letter to Culture, Media and Sport Secretary Jeremy Hunt which was made public this week.
The letter, dated 21 March, said waits in excess of an hour might deter tourists from returning to the UK.
The government sets BAA targets for processing departing passengers through security but no contractual service level agreements are in place for arriving passengers, said Mr Baugh.
He said the Home Office sets an "aspirational" waiting time of no longer than 45 minutes for non-EU passengers and 25 minutes for EU passengers.
Mr Baugh said: "That bears no relation to customer experience."

The project, called Historical Dances in an Antique Setting, is the work of Argentine artist Pablo Bronstein.
Three classically-trained dancers will be seen weaving up and down the Duveen Galleries "striking elegant and refined poses".
The free installation opens on Tuesday with live performances from 1100-1700. It runs until 9 October.
Bronstein's work also features two large-scale architectural structures which are overlaid with images of Tate Britain's exterior architecture.
The effect is described as "visually turning the gallery inside out".
"Grand architecture is one of the things I'm most interested in, so it was a rare opportunity to be able to create work in such a unique setting as the Duveen Galleries," Bronstein said.
"The commission also presented a perfect and challenging opportunity to work with performance on a large scale."
Tate Britain director Alex Farquharson said: "Pablo Bronstein's work consistently makes for deliciously jarring encounters between past and present, and between art and society. It's fantastic to see his work come to life in the aesthetic and institutional grandeur of Tate Britain's Duveen Galleries."
Passengers have faced waits of more than an hour at passport control at London's Heathrow Airport two days after it was revealed MPs warned it may struggle to cope during the Olympics.
[NEXT_CONCEPT]
A trio of dancers are to perform inside Tate Britain as part of the London gallery's latest commission.