Tory critics claimed that during his time as Agriculture Minister, Dr Cunningham breached rules obliging ministers to ensure they travel by the most cost-effective means.
The allegations surfaced as Tony Blair sought to put the upheavals and turmoil of the Christmas recess behind him by pledging that his Government should be assessed on its record on health, education and reform of the welfare state rather than "scandal and gossip" about individual politicians.
The row erupted after Nick Brown, Dr Cunningham's successor at the agriculture ministry, released details in response to a parliamentary answer showing he had used private jets for seven journeys to Luxembourg, Strasbourg, Rotterdam and Bonn although there were several scheduled flights a day.
The cost of these flights was as much as pounds 6,560 when the average fare for a business return would have been pounds 438.
Mr Brown made clear no private jets had been used by the ministry in the last year of Tory rule nor had he himself used a private jet since taking office.
Tim Yeo, shadow Agriculture Minister, said Dr Cunningham, Cabinet Office Minister, had "been caught with his snout in the trough". He added: "It appears his penchant for travelling on private jets instead of using scheduled flights, like every normal person, has cost taxpayers thousands of pounds."
But a Cabinet Office spokesman insisted Dr Cunnigham had acted within the rules under which travel arrangements are made to maximise the amount of meetings a minister can attend. In a separate development, Gordon Brown, the Chancellor of the Exchequer, was facing demands for a Downing Street inquiry about his ministerial conduct after reports that the PR firm HMC, partly run by his girlfriend Sarah Macaulay, had been paid pounds 100,000 to promote the New Statesman, owned by former Paymaster General Geoffrey Robinson.
David Heathcoat Amory, the shadow Chief Secretary to the Treasury, said Mr Brown was "driving a coach and horses" through the ministerial code of conduct.
He questioned whether the Chancellor knew about the commercial connection when he tried to persuade the Prime Minister last year to keep Mr Robinson in his job.
Mr Robinson resigned on 23 December, blaming his departure on 12 months of "a highly charged political campaign" by the media.
In his criticism, Heathcoat Amory pointed to the ministerial code of conduct under which ministers must guard against any risk of a potential conflict of interest affecting themselves or their spouse or partner.
"It is becoming clear why Mr Brown was so keen to keep his crony in place - not just to thank him for past favours but to keep his partner in style to which she had become accustomed," he added.
Critics argue that Charlie Whelan, the Chancellor's press secretary, fuelled rumours about the close links between Mr Brown and Mr Robinson last week when he allegedly joked that he could get a copy of the New Statesman before it was published because the Treasury "owned" the magazine.Reuse content