Ali Adnam Khan and Ikhlaq Hussain, both 29, were arrested on December 16 in the New Leeds area of the city.
They had been travelling in a car which failed to stop for officers and then rammed a number of police vehicles in pursuit.
During the chase, a Walther handgun loaded with seven rounds of ammunition and 46 separate rounds of 9mm ammunition were thrown from the vehicle.
Both Khan and Hussain were charged with the illegal possession of a Section 5 firearm and ammunition, and Hussain was additionally charged with dangerous driving.
Investigations by the National Crime Agency’s Armed Operations Unit showed the pair had met with two other individuals prior to the police pursuit and officers believe this was when the handover of the weapon and ammunition took place.
Four men have been jailed after pleading guilty to the illegal possession of a firearm and ammunition following an investigation.
As a result, Kyle Stewart was produced from HMP Leeds and Umar Mahmood was produced from HMP Lindholme so that they could be charged with conspiracy to supply a prohibited weapon and conspiracy to supply ammunition without a certificate.
Hussain pleaded guilty to all charges he faced in July, but the remaining defendants waited until the start of their trial on December 4 to plead guilty to conspiracy to transfer a prohibited weapon.
Today, the men appeared at Leeds Crown Court where Hussain, of Chesham Fold Road, Bury, was sentenced to six years and banned from driving for five years.
Khan, of Hartman Place, Bradford, was jailed for five years and 10 months, while 24-year-old Stewart and 31-year-old Mahmood had sentences of six years and three months and five years respectively added to their existing jail terms.
Tim Gregory, from the NCA’s Armed Operations Unit, said: “Firearms pose a serious threat to the safety of the public. As has been shown here today, the NCA and partners will not stop in our efforts to remove these dangerous weapons from the streets of the UK.
“We are actively sharing information with partners, taking action against those who seek to supply illegal firearms and removing them from criminal circulation.”