John Onyenaychi cut PC Paul Madden's throat and slashed at community support officer Piotr Dolata in Ealing.
The Old Bailey heard the attack was the culmination of a five-day crime spree by the 30-year-old last December.
Onyenaychi, of Wise Road, Stratford, east London, was found guilty of two counts of attempted murder and of attacking a third officer.
As well as the attempted murder charges, Onyenaychi, who received a life sentence, was convicted of causing grievous bodily harm with intent, robbery and attempting to cause grievous bodily harm.
The court heard the defendant cut PC Madden's throat as people watched and then lashed out with his knife at other officers who tried to restrain him.
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It's very humbling that my intervention perhaps contributed to the outcome of possibly saving [this officer's] life”
Samad Tadjkarimi
PC Madden's life was saved by retired heart surgeon Samad Tadjkarimi who happened to pass the scene as he was Christmas shopping.
Mr Tadjkarimi, who had retired from Harefield Hospital three weeks earlier, told the court he saw the officer lying on the ground with "lots of dark blood on the right side of his neck".
"I turned my attention to him immediately and I compressed his neck, holding it," he said.
"It's my duty, I guess. I'm sure anyone in my profession would do the same.
"It's very humbling that my intervention perhaps contributed to the outcome of possibly saving his life - a very brave young officer."
PC Madden, 23, received emergency surgery for injuries to his neck, throat and face. He was left with permanent scarring.
PCSO Dolata had to have 12 stitches to his head
The Recorder of London, Judge Peter Beaumont, said Onyenaychi had not shown any remorse.
He added: "He used a knife on the face and neck of a police officer who was doing his job.
"Paul Madden would have died with 2-3 minutes - such was the loss of his blood - without the help he received from the passing retired doctor."
The jury heard that minutes before the attack, Onyenaychi had become agitated when challenged about his ticket on a bus in New Broadway.
Support officers called to the scene recognised him as a man who was wanted for a previous attack.
PC Madden, who thought Onyenaychi might be armed, was stabbed as he tried to arrest him.
The trial heard the defendant was on licence at the time, having been jailed for two years for causing death by dangerous driving while under the influence of drugs.
He had previously attacked a prison officer, using a pencil as a homemade weapon, and committed other violent offences.
Det Ch Insp John McFarlane said: "He is one of the most dangerous men in Britain."
He refused to come out of his cell throughout his trial.
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