It was revealed yesterday that Mr Davis, who earns pounds 84,000 a year, had accepted four helicopter flights from the company and stayed in the Long Island home of one of GTECH's directors. Earlier in the week, he told a Commons committee that he had accepted five free flights across the United States in a private jet owned by the company.
Senior MPs on both sides of the House believe that these revelations make the regulator's position untenable.
But Mr Davis, at his luxury home in Wimbledon, south-west London, said yesterday: "I have no intention of resigning. I have no reason to resign." He then left to watch Wimbledon FC.
However, if he does not leave voluntarily, Mr Davis may well be sacked. His political boss, Virginia Bottomley, the Secretary of State for National Heritage, will be anxious to show that she is dealing with the situation firmly when she faces questions in the Commons tomorrow.
In the morning her officials, led by Hadyn Phillips, the permanent secretary, will be interviewing Mr Davis formally about his links with GTECH, the provider of Camelot's technical expertise, which has been investigated for corruption in the US.
Jack Cunningham, the Shadow Heritage Secretary, said last night: "It is increasingly clear that Mr Davis is, at the very least, guilty of exceedingly poor judgment. I will be raising his position again in the Commons."
Mr Davis was also criticised last week when Richard Branson, the chairman of Virgin, claimed on BBC's Panorama that he had been offered a bribe by GTECH's chairman, Guy Snowden, to drop his own bid to run the Lottery. Mr Branson claimed that he informed Oflot. Mr Davis denied he was aware of the allegations, and is taking legal action.
Some ministers are angry about what they say is a deliberate attempt by Richard Branson to destabilise the position of Camelot, which triumphed over Mr Branson's rival bid to run the Lottery without profit. "Nobody is going to be pushed around by Mr Branson," said one Government source.
But the past week has been deeply embarrassing for the Government. The various revelations have brought into question the award of the contract for running the National Lottery, the need for it to be profit-making and the adequacy of the regulatory regime. Mrs Bottomley's advisers are anxious to lift the cloud growing over the Lottery which, given its popularity, might have been a much-needed success story for the Government. "Above all, Virginia is concerned with the integrity of the National Lottery," said one insider at her department. "That is her first consideration."
Government ministers accept that, while Mr Davis's personal honesty is not being questioned - he is described as "a straightforward, sound and responsible person" - his conduct looks, to the general public, highly questionable. A Government source said yesterday that his contacts with GTECH and free flights were careless and unwise for a man in a regulatory position: "We live in a world where perception is often as important as reality."
Despite Mr Davis's public statement yesterday, the Department appears to expect him to offer his resignation voluntarily.
Tomorrow Dr Cunningham will call on the Government to establish a Code of Conduct for all regulators of public service business. "It is time to set out clear Codes of Conduct for all regulators to conform to in the conduct of their public duties," he said.
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