Several hundred of its cabs are operating in the United States, with smaller numbers working in dozens of countries including Canada, Singapore, Kosovo, South Africa, Cyprus, Saudi Arabia and Lebanon.
Azerbaijan is expected to order 1000 for its capital, Baku.
The first Australian shipment of 98 cabs for Perth has arrived, with a total of 200 planned for a four-year trial in the city.
"The response has been phenomenal," London Taxi Company Australia's chief executive, Evan Simeon said.
"We couldn't have asked for a better welcome. One Perth operator who purchased a fleet of the 50 bright, white used TX4s has already had a stampede of drivers who want to be the first ones to buy a cab and partake in the trial.
"We've had a lot of positive interest from expats, both prospective customers and drivers."
"What has been especially gratifying are the offers from ex-pat London Taxi drivers who not only want to buy one, but have also offered their services to train our Australian drivers on everything from the service to vehicle operation."
Perth's London cab drivers will be given back their weekly A$200 licence fee for the duration of the trial in return for vehicle and usage data under a WA Government-funded package.
By the time the trial ends they will have recouped most of the cab's cost.
The Victorian Government has also offered a A$20,000-a-year subsidy for the first 50 cabs on its streets.
The Perth trial is a major step in London Taxi's revival after steering problems, falling sales and plunging profits last year forced the recall of 400 cabs and pushed the company into administration.
The Coventry-based group was rescued by Chinese car manufacturer Geely Holding Group, which now builds export versions in its Shanghai plant.
