A year ago, the progress of Crossrail 2 seemed assured. A political consensus was forming that a second mass-transit line across London should be built from north to south, its urgency underpinned by the verdict of the National Infrastructure Commission (NIC) that this was the most important single project for Britain and work needed to start now. The then chancellor George Osborne duly doled out £80m to get the ball rolling, expecting a hybrid bill in the same parliament.

Now, with its champions having gone after the EU referendum, the project’s prospects look bleak. While City firms discuss relocating offices and staff, any assumption that higher business rates and commuter revenues would pay the £32bn construction bill is on shakier ground.

The omission of Crossrail 2 from the Conservative manifesto, in which other infrastructure projects were listed, was the clearest sign yet that there is little appetite in a Theresa May government for another London-based scheme. Although official reaction appears muted, constrained by the purdah rules of the pre-election period, insiders at Transport for London (TfL) fear that a cherished – and for them, critical – scheme is on the rocks.

The arguments for the north-south line, which would be tunnelled from New Southgate and Tottenham Hale to Wimbledon and link up with commuter rail services in Hertfordshire and Surrey, boil down to capacity. The arteries of the growing capital can only be temporarily unclogged through improving present lines. On the underground, the Victoria line has been upgraded and the Northern line is following, while an upgraded Thameslink service will also move extra passengers more swiftly through the centre of the capital.

With such upgrades and the imminent completion of the original Crossrail as the east-west Elizabeth line, some may think Londoners should shut up and be grateful. But the case for a new, faster service on this alignment was first made when the city was in relative decline: the Chelsea-Hackney line’s underground route has been safeguarded for decades. And now, with London’s population forecast to rise to 10 million by 2030, the picture is further complicated by the building of HS2, the high-speed rail network linking London to Birmingham and the north.

The previous London transport commissioner Peter Hendy warned for years of the mayhem to be expected at Euston when thousands of HS2 passengers pour into an already overcrowded rail terminus. More recently, London’s mayor, Sadiq Khan, said the city would “grind to a halt” without Crossrail 2. The scheme is seen by transport planners as vital to relieve the pressure on South West Trains, with its Waterloo terminus already the busiest station in the country.

Some renewed political impetus is expected after the election, when the NIC chairman, Andrew Adonis, a prominent champion of the scheme, is expected to return to public life and push its claims.

But since Lord Adonis’s commission pinned its colours to the mast, the Brexit vote has reinforced political wariness of looking London-centric.

David Leam, the infrastructure director at business group London First, said: “The key thing this project needs is a comparable one to start in the north. Crossrail 2 has a great case, but what the government also wants to do is to be seen to be investing in projects in the rest of the country.”

That equivalence is underlined by Labour’s commitment to building a “Crossrail of the north”. But even the nomenclature in the various manifestos is telling, Leam said: “It’s indicative of how ill-formed those ideas are that the [northern] scheme doesn’t really have a name: the Lib Dems talked about HS3 and the Tories talk about northern powerhouse rail.”

The politics are sticky. TfL has submitted a business plan for a scheme that had the full backing of the previous London mayor and transport secretary. But the antipathy between Khan and Chris Grayling has already emerged, with the latter rebuffing TfL’s business case for taking over inner London rail services on Southeastern, and at least part of the hold-up on Crossrail 2 appears to be TfL’s plan lingering in Grayling’s intray.

A government response was expected in early spring, but now autumn appears to be the earliest time for an announcement. Publication of the response may ease worries in Chelsea, west London, where many residents have opposed the building of a Kings Road station. With TfL looking to rein in costs to persuade the government, the station is strongly tipped to be excluded from the next iteration of the scheme.

Funding is also a stumbling block, because the capital will again be expected to meet at least half the costs, although business rates will remain elevated for years just to pay for the first Crossrail. Proponents of Crossrail 2 argue that revenue is guaranteed: this is a scheme to cope with demand, not one to stimulate economic growth, although it would also expect to fuel development, growth and housing further out on regional branches south and north.

“It’s not a build it and hope they come project. It’s as close to a sure thing as you can get in infrastructure,” Leam said.

The original Crossrail is scheduled to come into full operation within two years: its tunnels are built and the first trains will soon enter service on eastern and above-ground routes. Crossrail’s protracted genesis shows the £14.8bn project was far from inevitable: first outlined in the 1970s, it was backed in the 1990s by the government, before being scrapped, and was put under review by the Conservative-Liberal Democrat coalition as late as 2010, when construction had started.

Leam said: “We’re stuck at a red light, not shunted into the sidings. But we could be stuck there for five or 10 years. The risk is that we repeat the Crossrail experience of endless prevarication, while congestion gets worse and the cost goes up.”