The company was founded by John Griffin in 1975 with one car, the British Broadcasting Corp. reported Saturday.
"From humble beginnings about 40 years ago, Addison Lee has grown to become a well-known brand," said Griffin's son, Liam Griffin.
The equity firm said it wanted to expand the brand "both in the UK and internationally."
John Griffin will stay on as chairman. Liam Griffin will keep his position of chief executive officer.
The Daily Telegraph reported John Griffin started Addison Lee after cutting short an apprenticeship as an accountant to help out at his father's taxicab business.