They were chosen because of concerns about their business activities.

Six of the 12 did not respond and one said his contacts were not “for sale”.

Mr Straw and Sir Malcolm agreed to enter discussions with the fictitious Chinese company looking to expand its business interests in Europe.

Last year Sir Malcolm registered earnings of £69,610 — more than £1,600 an hour — from his work outside of Parliament, while Mr Straw earned £112,777 from his outside business activities.

Analysis by this newspaper of MPs' overall earnings showed they made more than £7.4 million from outside work in the past year. The Chinese “company” wanted to form an advisory board. Undercover reporters met Sir Malcolm at the fictional firm’s Mayfair office in January. Sir Malcolm, who served as foreign secretary under Sir John Major, described the access he could offer.

He said he could meet “any ambassador that I wish to see” in London. “They’ll all see me personally”, he added.

“That provides access in a way that is, is useful”.

In a second meeting, Sir Malcolm suggested that he would be willing to write to ministers on behalf of the company without declaring the name of the firm.