A banned activist was able to fly into the UK because of failings in a multi-million pound computer system designed to protect national security.
A Border Agency insider claims Sheikh Raed Salah's name was flagged up by the e-borders database, but could not be transferred to staff electronically.
Instead the alert system relied on bits of paper, which were passed to immigration officers at the wrong Heathrow Airport terminal.
The Home Office is investigating.
Although it has not commented on the specifics of that case, it has acknowledged there have been other instances of people getting through immigration control who should not have.
The Heathrow insider said he believed half the people named on these "stop lists" or "warnings index" were not turning up.
Sheikh Salah, an Arab-Israeli activist, flew into the UK last month, days after Home Secretary Theresa May had signed an order denying him entry to the UK.
He was expected to land in Heathrow's Terminal 1 on a flight from Tel Aviv, Israel.
The source told File on 4 that a paper alert was circulated to staff there but the flight disembarked at Terminal 5 instead and Sheikh Salah walked through unchallenged.
He attended a meeting in Leicester before being arrested by police and is now being held while arrangements are made for his deportation.
He is from a mainly Arab town in Israel and is the leader of a branch of the Islamic Movement.
The movement, whose stated aim is to advocate Islam among Arab Israelis, offers education and social services and promotes a Palestinian nationalistic stance.
The Home Office has not expanded on the reasons why he is not welcome in the UK.
The details of people who are deemed to pose a risk to the UK are kept on a database at what is known as the National Border Targeting Centre (NBTC), which is housed in a non-descript two-storey building near Manchester Airport.
The NBTC is at the heart of the £1.2bn e-borders programme. It carries out intelligence checks on air passengers as they fly into the UK.
Personal details are checked against watch lists of known criminals, immigration offenders and people thought to be a security threat.
Earlier this year, the Home Office revealed it has led to the arrest of 3,100 criminals since it went live just over two years ago. Analysts at the centre also look for suspicious travel patterns.
The government says the NBTC is a key element of its counter-terrorism strategy and in combating illegal immigration.
But the BBC has been told that information from the NBTC cannot always be immediately uploaded onto the computers used by front-line Border Agency immigration staff.
One officer, who works in one of the busy immigration halls at Heathrow and asked not to be identified, said: "We have no joined-up thinking in our system. It's as simple as e-borders will phone, say to the duty office 'This is what we are looking for'.
"They can't sit there and instantaneously put it on. We're running on a very antiquated system."
He said when the alerts come through from the NBTC, they are distributed on small slips of paper which can get lost.
He said: "A chief immigration officer or duty officer from the back office will come out with slips of paper, nothing more technical than an A4 sheet spliced into 20 or 30 slips, finger width, placed across your desk to look out for this individual."
The border officer said the result of the system is that they miss some individuals they should be preventing from coming into the UK - or at least, quizzing more closely.
Another officer described the system as "ridiculous" and "really low-tech and very easy to go wrong".
The Home Office said in a statement: "Anyone listed on a watch list should be flagged on entering the UK and questioned or refused entry, as necessary.
"We are aware of a few instances where this has not happened and these have been investigated and lessons learnt are taken forward."
Immigration Minister Damian Green said he was unaware that some alerts were being circulated on paper.
"If people want to produce evidence to me, I will look at it," he said.
File on 4 is on BBC Radio 4 on Tuesday 12 July at 2000 BST and Sunday 17 July at 1700 BST. Listen again via the BBC iPlayer or download the podcast.