Manchester City Council gave the green light for Allied Vehicles taxis to be used after the local authority effectively suspended its existing rules.
A maximum vehicle turning circle of just 25ft had prevented the company from supplying Manchester's taxi drivers because Allied's wheelchair-friendly vehicles are slightly larger than a London-style cab.
But now this rule has been suspended.
The council has changed its approach due to concerns that the collapse into administration of Manganese Bronze, the dominant supplier of London-style cabs, is hindering the supply of spare parts and new vehicles.
Paul Nelson, managing director at Allied Vehicles, whose headquarters are in Possil, said: "They have realised the world has changed a little bit."
He said Allied could snap up as much as 40% of the Manchester market, where some 1250 cabs operate.
Mr Nelson said he expected Allied to create 20 to 30 jobs to cater with the upturn in business. It currently employs 370 people.
Nigel Murphy, of Manchester City Council, said: "A review of our current hackney carriage licence policy will take place over the next six months."
In the meantime, the city has agreed interim measures in which a group of council officers and elected members will consider applications for taxi licences.
Previously it used the same rules as Transport for London, which included the requirement taxis complete a turning circle within a space equivalent to that available outside the Savoy hotel on The Strand.
Allied has already lent 20 taxis to drivers in Edinburgh and Glasgow whose Manganese Bronze vehicles have been taken off the road.