The PFP, the go-between for the Government and the private sector over the PFI, wields considerable power in directing the development of the PFI.
Senior officials at several construction companies have expressed their displeasure at what they see as her inflexibility, and non-interventionism, which precludes the injection of government funds into PFI schemes.
The criticisms come at a time when there have been several well-publicised withdrawals by contractors from PFI schemes. Recent problems are concentrated in the health trust sector, which has been dogged by problems of "staggering complexity".
Roads and prisons, by contrast, have had a relatively smooth passage. Unlike the Home Office, for prisons, or the Highways Agency, where there is only one contractor, each health trust is autonomous.
One source said that Ms Masters was almost universally disliked among construction companies. Described as fiercely anti-interventionist, "she sees it as her duty to prevent a single penny of government money being spent on these areas", the source said.
Dame Sheila has substantial influence on the PFP, particularly in the area of health trusts. A partner of accountancy firm KPMG, she was seconded as director of finance to the National Health Service from 1989 to 1991, and later served on the NHS Policy Board. She is also a non-executive director of the Inland Revenue's Management Board, and the Bank of England.
Her time at the NHS was one of root and branch reform, where she introduced tough financial controls. She has said the prevailing NHS culture on her arrival was "one of fiddling to get round the year and borrow off next year". Her intimate knowledge of the health service, coupled with her strong views on its management, means her views are taken seriously by the Government and her colleagues on the panel. Dame Sheila was unavailable for comment.
Jennie Price, director of the Major Contractors Group, which represents the 22 largest construction companies in the country, said there were several concerns for its members. "PFI is exercising our chief executives and chairmen more than any other single issue at present," she said. Although there seems to be a growing belief that the future of the PFI is now assured, it is clear that abundant teething problems remain.
Last year the PFI was revamped, with a clear mandate for the burden of funding to be borne by the private sector alone. Construction firms are unhappy about the development, which replaced a previous agreement where the Government would share some costs. They are particularly irate about the enormous cost of tendering for a PFI development, which can cost up to pounds 2.5m to table a realistic bid - far in excess of other private-sector tenders. They argue that for such sums, failed bidders should share the cost with the client. Further complexities include the long time-frames of the projects - often up to 30 years.
"The frustration on the contractors' side is that Dame Sheila has a strong commitment to the new principles without the appreciation of the benefits a little capital feeding could have," Ms Price said. However, she added, the construction industry continues to lobby the Government for change, and there are signs of progress.
Stephen Dorrell's Department of Health now has more than 40 health trust hospital developments, worth some pounds 500m, mired in the complexities of agreeing details before contracts can be signed.
Not all contractors are against the Government. Michael Laycock, chairman of Taylor Woodrow Construction, says he can understand their stance. "Any funding might create a precedent, and they fear that would lead to the floodgates opening," he said. He also emphasised that consortia proposals must be properly costed and argued. Taylor Woodrow is the lead contractor for a South Bucks health trust hospital, which looks likely to be first past the finishing post, when a contract is signed, probably by Christmas.