Acourt, 42, and brother Neil, 43, who was another Lawrence suspect, headed a gang which moved resin worth £7.4million between London and the north east between 2014 and 2016.
Jamie had denied the allegations but changed his plea on the second day of the trial.
Crispin Aylett, prosecuting, told the court Acourt now admits involvement in 28 trips which shipped drugs worth £5.6million.
Jamie fled to Spain in 2016 after police arrested several suspects, including Neil's father-in-law Jack Vose, 65, in South Shields, jurors heard.
When officers went to Jamie's home in Bexley, south-east London, he had already vanished.
Officers broke down the door to get in and while they were there his partner Terri-Ann Dean arrived at the flat.
She was told to get Acourt on the phone and he was told by the officers he should either come to the flat or turn himself in at a police station.
But Acourt was on the run in Spain and lived in the trendy Diagonal Mar district of Barcelona, until he was finally arrested in May this year as he left a gym.
He was living under the name Simon Alfonzo and had a passport in that name.
Jurors heard his brother Neil, now known as Neil Stuart, is one of six men who have already been convicted and sentenced over the plot.
Couriers made the 600 mile round trip to South Shields to deliver drugs, collect money, or both and 34 journeys were made over the two year period.
Once the money was collected, it was handed to Jamie or Neil back in southeast London, he said.
Some of the delivery men were the fathers of their respective partners.
One of the conspirators, Lee Birks, is the father of Jamie Acourt's partner and another, Jack Vose, is Neil's father-in-law.
Another delivery men, Darren Thompson, was arrested in May 2015 as he was about to take delivery of 100 kilos of cannabis worth £200,000.
Vose was found with 100 kilos of resin in South Shields on 1 February, 2016, the court heard.
Neil Acourt, Vose, 57-year-old Birks, Paul Beavers, 51, Thompson, 30, and James Botton, 46, have all been convicted of conspiracy to supply class B drugs and sentenced.
Stuart, of Eltham, was jailed for six years and three months. Vose, of Bexley, was jailed for four years and nine months.
Thompson, of South Shields, Tyne and Wear, was jailed for four years and two months. Beavers, of Newcastle, was jailed for three years and four months.
Botton, of Greenwich, was jailed for four years and nine months.
Acourt and brother Neil, were among five men named as suspects after Stephen Lawrence was knifed to death in a racist attack at a bus stop in Eltham, southeast London, in 1993.
They have always denied any involvement in the killing.
Acourt, of no fixed address and formerly of Bexley, initially denied conspiracy to supply cannabis but admitted it this afternoon after the prosecution finished opening the case against him.
He will be sentenced tomorrow.
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