Some committee members, including Labour's Peter Shore, MP for Bethnal Green & Stepney, and the Liberal Democrat peer Lord Thomson of Monifieth, are understood to have argued forcefully in favour of such an investigation.
But after more than three hours of what Lord Nolan called "full and frank" discussion on its future work, members eventually emerged to unanimously rule it out.
A prepared statement made clear, however, that "as noted by the chairman when the committee was set up, certain aspects of party political funding do fall within its terms of reference.
"It would be wholly wrong for political parties to seek or accept funds against an expectation of, or following, the award of public office, honours, contracts or improper influence."
The statement said that the committee took into account "the intensely party political nature" of the issue.
Echoing remarks by Lord Parkinson, a former Tory party chairman, on Monday, it said: "Because any study would inevitably take place during the run-up to the next general election, it would be impossible at this time to review political funding in a non- partisan fashion."
Jack Straw, shadow Home Secretary, said Labour deeply regretted Lord Nolan's decision, "especially as he clearly accepts that he can and should look into the subject.
"The general election may be as much as two years away. There is ample time for a report to be produced, and people in this country would want to know Lord Nolan's recommendations before the election, not after it."
Speaking after yesterday's meeting, Lord Nolan denied the committee had "caved in" under pressure from John Major, who yesterday stuck by his opposition, insisting that making donors declare donations to parties would eventually lead to funding parties out of taxpayers' money.
Lord Nolan said: "We feel it would do more harm than good to try and tackle this in the run-up to an election. It would be politicially divisive and we would be right in the middle of the party political arena."
Mr Major yesterday sought to castigate Labour for failing to implement a code of practice recommended by the Commons home affairs select committee which had dealt with the whole issue 18 months ago. This says substantial anonymous donations should be refused and illegally obtained money returned.
His claim that the Tory party had implemented in full such a code was dismissed by John Prescott, Labour's deputy leader, who said: "The Tory party refuses to divulge details of donations they receive, many of which are undoubtedly substantial."
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