According to a report in the Sunday Times, Tony Elliot has written to the OFT out of frustration over the lack of detail provided by the BBC over its trading relationship with .
Elliot's letter reads: "The BBC's Fair Trading Guidelines require all transactions...to be based on formal agreements which must be transparent. However, these are not available and from the announcements at the time of the acquisition apparently none are contemplated."
The BBC's commercial arm BBC Worldwide paid £75m in October 2007 for 75% of Lonely Planet to its founders Tony and Maureen Wheeler.
John Smith, the BBC Worldwide chief executive, said at the time that the deal fit Worldwide's strategy "to create one of the world's leading content businesses, to grow our portfolio of content brands online and to increase our operations in Australia and America".
Elliot called for Worldwide's activities to be reined in, saying: "BBC Worldwide, from a lot of people's point of view, is out of control. Somebody needs to really have a close look at it and define what it really should be doing."
Time Out's frustration with the BBC's lack of disclosure about the deal is reportedly also shared by Penguin, which owns the Rough Guide imprint, but also has a joint venture with the BBC to publish children's books.
Penguin requested further details from the BBC Trust last October, under the Freedom of Information Act, on how the Lonely Planet deal was endorsed and how the company would operate in future.
It is now considering its next move, which may be to complain to the Information Commissioner.
Time Out's attack on BBC Worldwide follows recent criticism of the BBC by the BBC Trust for overspending by £36m on .