The Government must meet its HS2 underspend target if it is to win public support for the flagship infrastructure policy, which is to link London with Birmingham, Manchester and Leeds, a Labour MP has said.

Susan Elan Jones attacked what she called the "London-based commentariat" for seeking to build public opposition to the scheme, but warned the Transport Secretary that failure to make sure it comes in under budget would be seized on by detractors.

"France, Germany, Japan and many other countries of course have benefited hugely from their high speed rail links, and I think that many of us are quite fed up with a largely London-based commentariat that is seeking to stop a north-south high speed rail link in this country," said the member for Clwyd South.

"Do you agree ... that it is extremely important, if we are to build a better consensus in this country, that those budget figures will be met and we will be able to keep monitor on that?"

Ms Elan Jones' comments followed an assurance by Transport Secretary Patrick McLoughlin that HS2 would come in for less than originally anticipated .

Speaking during Transport Questions in the Commons, he said: "The spending round of 2013 set a long-term budget for the delivery of HS2 of £42.6 billion. This is made up of £21.4 billion for phase one, and £21.2 billion for phase two.

"The budget includes a significant level of contingency provision of £14.4 billion. This budget is being tightly monitored by the Government and is confident that the railway will be delivered for less than this.

"I have set HS2 a target price for phase one of £17.1 billion."

Former Welsh Secretary Cheryl Gillan expressed the scepticism shared by many opponents of the project.

Ms Gillan, who stood down from her Government post to fight HS2 which is expected to run through her Chesham and Amersham constituency, said Mr McLoughlin had lost control.

"You were forced this week to launch a so-called fightback with a piece of expensive and self-satisfying research from KPMG on HS2 because you have lost control of the budget, you have lost control of the arguments, including the need to travel at speeds in excess of 250mph.

"I think it's about time we replace HS2 with a thoroughly researched and integrated transport strategy for all regions, including Wales, and covering air, road, rail and communications links . When will you cancel this project and produce a decent, overall strategy?"

However, Mr McLoughlin defended the report on the economic benefits of building high speed rail.

"I'm not sure I was forced to do anything," he said.

"What I was asked to do by the Public Accounts Committee was to do a proper research into and to back up the case for HS2.

"And I daresay that if yesterday's report had come out negative all those people against HS2 would have been shouting it from the rooftops, because it came out positive they are opposed to it."