The criticism comes in the wake of the problematic opening of T5
A senior executive at a major airline says London's Heathrow is probably the worst European airport it uses.
Don Langford, head of customer services Europe for American Airlines, said the site suffered from lack of investment.
The airport - recently criticised for the chaos at the opening of Terminal 5 - was "trying to put 10 pounds of sugar in a five-pound bag," he told the BBC.
But Heathrow operator BAA said things were improving and it would invest £4bn over five years to improve the airport.
Dozens of flights in and out of the new Terminal 5 were cancelled on its opening day last month when luggage handling problems caused thousands of passengers to lose their bags.
Mr Langford said in a File On 4 investigation into the first day chaos at Terminal 5, that Heathrow Airport, "is not just bursting at the seams. I think the seams have burst".
American Airlines claims to be the fourth largest carrier at Heathrow in terms of available seats and flies out of Terminal 3, which Mr Langford called "a bit of a dump".
He added: "It has suffered from lack of investment over a period of time.
"If you look at the fabric of the building, if you look at where customers check in - missing light bulbs, duct tape on the floor.
"I would have to say that Heathrow is in many ways the worst of all the airports that my company flies to in Europe."
But BAA's corporate affairs director Tom Kelly told the BBC, "This is an airport which was designed for something like 45 million passengers - we have now got 65 million.
"We are investing £4bn over the next five years.....you've got to realise that if you are going to invest that kind of money it takes time to put things right."
File On 4 was told that rehearsals for Terminal 5's big day had already revealed signs of problems.
And Mick Rix of the GMB union claimed the baggage system did not receive realistic enough tests prior to opening.
"I have been told that British Airways had severe reservations about the software that is being used on the baggage handling system - they found out later that the software problems were such that if the system had been tested correctly and for long periods of use they would have been spotted," he said.
One of 250 volunteers taking part in a dry run two weeks before the first working day, teacher Sue Knight from Hillingdon, Middlesex, spoke of the problems.
Her group was told to pretend they were transferring from a flight arriving from Manchester to a flight bound for America. A bus would take them to another terminal. The buses were supposed to pick up passengers every five minutes.
"A bus came after an hour and drove us around the terminal but by then we had missed the flight.
"I spoke to one lady who had been on the trial where she had been given luggage but hadn't got it back."
Peter Morris, chief economist of aviation consultancy Ascend said the Terminal 5 trials were on too small a scale.
However Tom Kelly of BAA said critics of the dress rehearsals were being wise after the event.
'No mess ups'
"We did 18 months of pre-testing. We had the services of some 17,000 volunteers and we processed literally thousands of bags.
"On any one day we had hundreds of people so we did test the system - I'm afraid it is one of those situations where it is very easy to be wise with hindsight."
Both BAA and British Airways have been told been by the Civil Aviation Authority (CAA) to produce urgent reports on the Terminal 5 problems.
Harry Bush, the CAA's head of economic regulation said: "We have said very clearly to both BAA and BA we want to see the lessons-learned exercise conducted very quickly because the next stage of modernisation at Heathrow is going to require a lot of different airline moves between the terminals at the east end of the airport.
He added: "We want to make sure the same mess-up doesn't occur there."
Hear the full story on BBC Radio 4: File On 4 Tuesday 29 April 2008 at 2000 BST, repeated Sunday 4 May at 1700 BST or online at the File on 4 website.