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The court heard O'Reilly caused a double smash.
Prosecutor Anthony Prosser said he first hit the rear of the Peugeot, causing it to spin and overturn onto its roof across the inside lane.
Mr Gregory was pinned upside down in the vehicle when another car, a VW Bora, was unable to avoid the Peugeot and also smashed into it.
Mr Gregory, who lived in Harris Road and was a dustman for Islington Council, died from multiple injuries. His passenger, work colleague Clifford Morris, was also injured.
The force of the impact with the Peugeot caused O'Reilly's rear nearside wheel to sheer off, leaving gouge marks in the road. He swerved across two lanes and came to rest in some bushes.
O’Reilly was arrested and a breath test proved positive.
Experts estimated his speed at the time of the accident was 69-75mph. "It must be taken as a minimum," said Mr Prosser. "It could be significantly higher."
"Some witnesses say as he approached junction five he was driving at excessive speed," he continued.
One later made the bat-out-of-hell comment, added Mr Prosser, and another, a railway engineer, said the car’s speed was "sheer lunacy". They soon afterwards arrived at the scene of the accident.
The court heard O’Reilly had come across from Ireland to Holyhead in Wales by ferry. He arrived at about 7.30pm on June 26 and reached the M2 at about 3.30am the following morning.
When interviewed, O’Reilly, who was visiting cousins in the Sittingbourne area, said he believed his car had been struck to the rear by another vehicle and maintained the crash was not his fault.
But there was no damage to the back of his car.
He said he only made two stops on the journey to fill up with petrol.
Judge Carey said O'Reilly was convicted on the clearest evidence of what was "a very bad case indeed" of causing death by dangerous driving.
He said that those who drink and drive put other road users at great risk and that drink-driving laws "properly reflect society's wholesale disapproval".
Judge Carey continued that it did not matter whether O'Reilly struck the barrier before careering into Mr Gregory or dropped off to sleep in his "tired and befuddled state" when judging his culpability.
He said having flipped the Peugeot over, it was "an innocent obstacle and target" for any on-coming vehicle and that the driver of the Bora had no opportunity to avoid it.
The judge said the three features of alcohol consumption, excessive speed and driving without a break put it into the highly culpable bracket. He added that it was most exceptional for a lifetime ban to be imposed in the UK.
"I would only impose it if I thought it was necessary for the protection of law-abiding motorists here. It is necessary."
Addressing the jury of seven women and five men Judge Carey thanked them for their close attention to what he described as a "troubling" case.
"It must give you no pleasure to return a verdict which leads me to impose a sentence of such severity as I have," he continued. "But we are concerned with a death, a loss of life.
"Although nothing can make up for that, or bring back Mr Gregory, society expects that those who cause the death of an innocent motorist will be severely punished and that is what I have to do."
In a victim impact statement Clifford Morris spoke of the friend he had known for almost 19 years and worked with for eight.
He described Mr Gregory as a good friend whom his children called "Uncle Andy." He would often have dinner with Mr Morris and his family, as well as accompany them on day trips, collect his children and help out with Mr Morris's elderly father.
As for Mr Morris himself, he stated that he was off work following the accident and is now nervous in cars. "I will sit in a stationary car but I am not confident when it is moving."
He added that he still suffers from pain in his side when turning a steering wheel.