Sajid Javid is expected to throw his weight behind the controversial HS2 rail project at a key meeting on Thursday, after the Treasury concluded it will still deliver economic benefits despite spiralling costs.

The chancellor is poised to tell Boris Johnson and Grant Shapps, the transport secretary, that he believes the sums still add up despite the price tag having risen to an estimated £88bn.

A final decision is unlikely to be made until next week – but with value for money the main source of concern inside government, Javid’s backing removes an important obstacle.

Allies of Javid said Treasury officials had been scrutinising the economic case for the plan – and that he had concluded there was little alternative given the government’s stated aim of “levelling up” regions outside London.

However, the chancellor is expected to demand tighter budget controls over future stages of the project. A National Audit Office report concluded last week that the final cost of the scheme was “impossible to estimate with certainty”.

Before December’s election, Johnson postponed making a decision about the future of the 250mph Y-shaped rail network, which would link London, Birmingham, Manchester and Leeds.

HS2 has long been politically controversial but Johnson has tended to support public infrastructure schemes in the past, and during the election campaign he called it a project of “great national importance”.

The prime minister has also faced enthusiastic lobbying in favour of the rail link from northern mayors, including Conservative Andy Street, the mayor of Birmingham, who called HS2 “a once in a generation game-changing investment”.

By contrast, a group of new Conservative MPs in “blue wall” northern seats have banded together to call for the project to be scrapped, and the money saved spent on smaller-scale infrastructure projects in the Midlands and the north.

But with the Treasury planning a significant increase in borrowing to fund investment, government sources suggest Tory MPs can be reassured that many of these projects may still be affordable even if HS2 goes ahead.

The Treasury is currently reviewing the way the government assesses the costs and benefits of public sector projects. Changes to the so-called “green book”, which sets the framework for officials to judge value for money, are expected to work in favour of schemes such as HS2, by allowing a wider definition of economic benefits to be included.

Johnson was asked by Conservative backbencher Kevin Hollinrake at PMQs on Wednesday: “Does the prime minister agree that we need to increase capacity in our railways in and between the north, the Midlands, the south and Scotland, and unless we want decades of disruption, the only way to do this through the Midlands engine rail, northern powerhouse rail and HS2?” He would only reply that an announcement would be made “very shortly”.