Passport officials also complained that angry travellers have tried to "storm" immigration controls without having documents checked.
Staff have reportedly been subjected to verbal and racist assaults and "slow-clapping" from passengers voicing anger at the delays.
Unions claimed arrangements had been put in place for extra police officers to be made available over the safety concerns.
"We are seeing public order issues in queues, including slow hand-clapping, abuse of staff and attempts to storm the controls, with people just trying to walk through without being checked, particularly at desks that are not manned," said Lucy Moreton, of the Immigration Services Union.
"They have negotiated with Heathrow for extra police to be around the halls. People want them to be more visible and to be sure that they can be quickly moved to areas where staff fear trouble. There are fears of public disorder."
The disclosures, reported by The Times, came as passengers faced "appalling" queues at Heathrow airport yesterday as the Border Force left half the immigration desks unmanned despite a pledge to cut delays.
Keith Vaz, chairman of the Commons home affairs select committee, said people were left "stacked" in corridors at 7am as Terminal 4 struggled to cope.
He voiced concern that Olympic officials and competitors had started to arrive a week before extra Border Force staff are deployed.
He demanded an explanation from the Border Force amid fears the chaos could hit the Olympic Games, which begin later this month.
"I was appalled by the length of queues in the immigration hall this morning," Mr Vaz said.
"It is now two months since the Immigration Minister promised additional resources and better management.
"The worst aspect was that half of the immigration desks were simply not opened even though the Border Force had prior knowledge of all flight arrivals."
He added: "This creates additional security pressures with luggage piling up in the baggage hall. We had people waiting in the corridors at the busiest international airport in the world."
According to BAA, which operates Heathrow, the Border Force yet again failed to meet its 45 minute maximum waiting time target for passengers from the European Economic Area - the EU along with Switzerland, Liechtenstein, Iceland and Norway.
Last week BAA released figures showing that the Border Force, which had promised to deploy extra resources, repeatedly failed to meet the benchmark it set itself.
Last week The Daily Telegraph found passengers were forced to wait more than two hours to get through border controls, in queues stretching for half a mile.
The delays at Heathrow have angered the aviation industry with senior figures describing them as an embarrassment to Britain.
Earlier in the year, in an interview with The Daily Telegraph, Willie Walsh - the head of BA's parent company, the International Airlines Group - warned the delays were discouraging major overseas investors from doing business in Britain.
The latest delays intensified pressure on Theresa May, the Home Secretary, for action with Yvette Cooper, her Labour shadow, failing to ensure that sufficient staff were deployed at peak times.
Damian Green, the Immigration Minister, defended the Government's record, insisting there had been significant improvements in the last two months and additional staff would be available during peak periods during the Games.
"But we're not complacent about some long waiting times, which is why this weekend we have increased staffing numbers by more than 50% at Heathrow to respond to large passengers volumes," he said.
"And by the start of peak Olympic arrivals in less than 10 days, there will be up to 500 additional staff on our rotas across the country - this includes enough staff at Heathrow to cover every desk during busy times.
"Additionally we have special lanes in place designated to Olympic athletes to enable them to pass through the border without delay."
Meanwhile, the interim head of the UK Border Force has not applied to take on the role permanently, the Times reported.
Brian Moore, the former chief constable of Wiltshire Police, took the role following the resignation of Brodie Clark last year in a row over the relaxation of passport checks.
Mr Moore's decision not to seek the job of Director-General of the UK Border Force on a permanent basis is an embarrassment for Ms May. He will continue as interim director-general until September.