London’s biggest minicab firm has been put up for sale by its private equity owner.

Carlyle Group paid £300m for a majority stake in Addison Lee in April 2013, but has decided to start an auction process after receiving unsolicited offers for the business, according to a source close to the company.

Private equity firms BC Partners, CVC Capital and Charterhouse are among the organisations that have been invited to bid, with reports suggesting the taxi firm could be sold for £800m. Carlyle and Addison Lee declined to comment.

Private equity firms usually retain investments for four to five years, but Carlyle is ready to cash in on Addison Lee’s strong performance.

The taxi business, founded by former cabbie John Griffin with a single car in 1975, ferries 10 million passengers around the capital every year, and is one of the main rivals to London’s black cabs, which have been battling strong competition from smartphone apps that allow people to hail any minicab at the touch of the button.

Addison Lee has expanded to Paris and New York and plans to launch in other cities, an investment that will be funded by any future buyer.

Griffin recently stood down as chairman of the company, which has trebled net profits to £16m in its latest financial year. Turnover has risen to £172m.

This article was amended on 23 September 2014 to confirm that John Griffin is no longer company chairman.