Despite his status at Minister of State level outside the Cabinet, 37 per cent said Mr Mandelson would be among those with "most influence over government policy during the next five years".
In a poll of 100 business leaders, civil servants, MPs, trade unionists and media editors carried out by Opinion Leader Research, Mr Mandelson pushed Robin Cook, the Foreign Secretary, and John Prescott, the Deputy Prime Minister, into fourth and fifth places.
The opinion leaders' panel was asked to name the three individuals they expected to be most influential. While Gordon Brown, the Chancellor, was named by 64, Mr Cook was named by 24 and Mr Prescott by only 11.
Unusually for a non-Cabinet member, Mr Mandelson sits on 11 of the 19 Cabinet committees set up by Tony Blair and last week he was appointed to take charge of the Millennium Dome project, which many Cabinet ministers want scrapped but which is close to the Prime Minister's heart.
However, when asked to rate which Labour politicians have been most impressive in the Government's early days, Mr Cook comes third, scoring 54, behind Mr Blair on 79 and Mr Brown on 77. Mr Mandelson, on 13, trails in fifth place behind Mr Prescott on 14. Mo Mowlam, Secretary of State for Northern Ireland, scored 11, and David Blunkett at education and employment scored 10.
Opinion-formers also expect the Government to carry through radical reforms of the welfare state, judging by the rating accorded to Frank Field, number two in the Department of Social Security, who scored nine for "most influential" and eight for "most impressive". Mr Field has called for a recasting of the benefits system to end its "culture of dependency".
The range of influences over Mr Blair's government is reflected in the three-way tie for seventh place in the influence rankings, with Bill Clinton, Helmut Kohl and Lord Irvine, the Lord Chancellor, each attracting seven votes.
The rating for Mr Kohl, echoing the Conservative advertisement during the election campaign showing Mr Blair on the German Chancellor's knee, no doubt reflects Euro-sceptic dismay at Labour's perceived pro-European stance (there were also two votes each for Kenneth Clarke and Jacques Santer, the European Commission President, and seven mentions of "the European Union", although panellists were asked to name individuals).
Derry Irvine is a more informed choice: the leading barrister has been a close confidant of the Prime Minister's since Mr Blair trained as a lawyer in his chambers in the Seventies. He played a central role in Labour's election team and now sits on eight Cabinet committees and chairs three of them. Our opinion leaders have an overwhelmingly positive and optimistic view of the new Government. By a margin of 77 to 7 they are happy with its performance so far, by a 58 to 29 majority they disagree that "sleaze has become an inherent part of the British political system", and by 63 to 17 they say Mr Blair is likely to succeed in cleaning up government.
They also expect the Labour government to fulfil all its five key pledges, even the general promise to "ensure low inflation, raise investment and strengthen the economy" - which 47 rated "likely" against 32 "unlikely".
Interviews were carried out from 9 to 16 June.
Power of persuasion: how they shape up
Who will be most influential over government policy?
1. Tony Blair - 83;
2. Gordon Brown - 64;
3. Peter Mandelson - 37;
4. Robin Cook - 24;
5. John Prescott - 11;
6. Frank Field - 9;
7. Bill Clinton -7;
Lord Irvine - 7;
Helmut Kohl - 7;
The EU -7.
Which Labour politicians have impressed most?
1. Tony Blair 79;
2. Gordon Brown 77;
3. Robin Cook 54;
4. John Prescott 14;
5. Peter Mandelson 13;
6. Mo Mowlam 11;
7. David Blunkett 10;
8. Frank Field 8;
9. Margaret Beckett 7;
10. Jack Cunningham 4.
Opinion Leader Research asked 100 opinion-formers to name their top three in each categoryReuse content