Hanson is one of the most likely bidders for the mines, and Martin O'Neill, the Labour Party's energy spokesman, is concerned about the potential conflict of interest.
Kevin Palmer, Rothschild's director specialising in the coal industry, said that if Hanson were to bid for the mines, the bank would 'not work both sides of the deal'. It would not continue to advise Hanson.
It has emerged that Hanson may already have put pressure on the Government to allow piecemeal privatisation of the pits so the company might bid for the best mines.
In 1990, Rothschild was an adviser to some of the privatised electricity companies, whose switch to gas-burning power hit the coal industry. But the company said it stopped working for the electricity industry when it became the Government's main adviser on coal.
Martin Taylor, Hanson's vice-chairman, said he would not comment on rumours. 'We have said that if the Government chooses to privatise British Coal, no doubt our mining interests in the United States will look at it.'
If the rumoured Hanson plan for sell-offs is taken up, it might speed up privatisation. But it would meet opposition from coal managers and some unions, which believe British Coal should be sold intact.