Two Boeing 747 jumbo jets have recorded an alarming near-miss while flying over Scotland, when pilots were told to take immediate evasive action – and instead turned towards each other.

Investigators have issued a damning report into the incident, expressing shock that all four pilots – two on each plane – either “misheard or misinterpreted” the clear instructions they were given.

Following an extensive review into the events of Sunday 23 June this year, it has been revealed that the two aircraft came to within 100ft vertically and less than 3 nautical miles horizontally – well under the minimum safe separation.

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The severity of the incident was classed as “high” by one of the pilots. Believing he was acting on safety instructions, he turned right only to see the other 747 straight in front of him.

Between them, the jets were carrying up to 1,000 passengers. The details of the incident were revealed by a report from the UK Airprox Board (UKAB), responsible for analysing all near-misses in the skies above Britain.

The two 747s were both in the process of preparing for transatlantic crossings – at the same altitude of 34,000 feet – as they were heading over Montrose airspace.

As their paths looked set to converge, Scottish air traffic controllers told the 747 on the left to turn left, and the plane on the right to turn right. Yet for reasons which remain unclear, the pilots followed each other’s instructions – and head on a collision course.

UKAB has released transcripts of the messages relayed to the pilots, which seem to show them correctly acknowledging the instructions before going on to make the same, potentially catastrophic error.

“Avoiding action [call sign of B747(1)] – turn left immediately heading 270 degrees, traffic in your right one o’clock,” the air traffic controller says. The pilot of B747(1) confirms he has heard – before turning right instead. He then relays a message to control saying there is “traffic in sight”.

One minute after issuing his first instructions, the air traffic controller changes tactic – and tells the pilot of B747(1) to “descend now immediately”, telling the other plane to go up.

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The situation was resolved by the shift in altitudes, and each 747 resumes its own course – but the Board questioned how the planes had come so close to disaster.

“It was apparent that both crews had taken each other’s instructions, and the Board found it hard to determine why this had occurred,” the report said.

“The Board was surprised that all four pilots had misheard or misinterpreted the avoiding action instructions despite at least one of the crews reading them back correctly.”

In discussing the incident, UKAB determined that the planes’ call-signs were not similar enough to be confused, and their instructions (which could be heard by all parties) were unambiguous.

They decided that no blame could be placed with the air traffic controllers – whose actions as things started to go wrong were deemed positive in preventing a collision.

Suggesting that the pilots may have been distracted by their preparations to cross the ocean, the board nonetheless determined “that the pilots’ actions, by flying each other’s avoiding action instructions” caused the incident.