Both companies refused to comment yesterday on reports that David Harding and Mike Smith, the respective chief executives, had hatched a £4 billion merger plan.

The plan is thought to have been rejected by William Hill’s board, chaired by Charles Scott, on valuation grounds.

Although both William Hill and Rank have similar stock market capitalisations, they trade on different priceearnings multiples.

William Hill is trading on a 14.7 times multiple based on this year’s profit forecast, and 12 times next year’s likely number. Rank is trading on a 17.4 times multiple for this year and 15.7 times for 2006, according to Hemscott, the financial data provider. The valuation difference means that Rank’s shares would be viewed as overvalued in a one-for-one share swap with William Hill.

It is thought that Mr Harding instigated the talks and remains on friendly terms with Mr Smith, despite the collapse of the talks.

Rank’s board, which is headed by William Cathcart, the Avis Europe chairman, is not thought to have voted on the William Hill merger proposal.

A merger would have combined William Hill’s eponymous bookmaking chain with Rank’s Mecca bingo, Grosvenor casinos and Blue Square online betting operation.

Under the proposal, Mr Harding would have become chief executive of an enlarged group that would rival Gala Group, the private equity-backed bingo and casino operator.

Rank is in the process of selling its Deluxe film and media unit for about £423 million.

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