The proposal to restore the route, which would branch off the existing Hull-Scarborough line, which passes through Beverley, is one of ten from Yorkshire and the Humber being analysed by technical advisers at the Department for Transport (DfT) and Network Rail.
Campaigners hope it will get funding in round three of the £500M Restoring Your Railway initiative which aims to reinstate axed local services and restore closed stations.
Other lines being considered in Yorkshire and the Humber include the service from Cross Gates in Leeds to Northallerton via Wetherby, Harrogate and Ripon, the Don Valley Line, the Upper Wensleydale Railway and the reinstatement of the North Midland Line between Barnsley to Wakefield via Royston.
So far successful bids from rounds one and two of the fund are the reintroduction of passenger services on the Barrow Hill line between Sheffield and Chesterfield and reopened lines and new passenger services between Gainsborough and Barton-upon-Humber.
All the round three bids will be assessed by an expert panel in June, including three Government Ministers, the Chair of Network Rail and Isabel Dedring, former London Deputy Mayor for Transport.
And the bid for funding would provide 75 per cent of the costs of a feasibility study, up to a maximum of £50,000. Officials from the DfT will then work alongside the project’s team to develop a detailed business case, the first step towards potentially obtaining funding for the project’s delivery itself.
Conservative MP for Beverley and Holderness Graham Stuart, one of a cross-party group of MPs backing the restoration of the Beverley-York line, said he had spoken to Rail Minister Chris Heaton-Harris about the scheme and was told it had potential.
Mr Stuart, himself a Minister in the Department for International Trade, said: "I’ve since met with the Minister for further advice, and we now also have international engineering firm AECOM assisting us.
“This has cross-party support all along the proposed line of route, in recognition of the fact that it would help to relieve traffic congestion and harmful emissions, boost job opportunities and tourism, and free up services on the existing routes out of Hull.”
The Yorkshire Post understands that AECOM, which describes itself as the world's premier infrastructure consulting firm, has been providing some consultancy work and advice as well as looking over the bid application to refine it and add their technical expertise
Before closure the route Hull–Beverley–Market Weighton–York had daily direct trains and was often referred to as the Hull to York line. The line was recommended for closure in the 1963 Beeching report and closed in November 1965.
A group, the Minsters' Rail Campaign, was established in 2001 to promote the re-opening of the line. If successful the line would stop at Market Weighton, Pocklington, Stamford Bridge and Haxby before arriving at York, and would also serve Cottingham and Hull Paragon Interchange.
The funding bid has been supported by MPs in both Hull and York as well as the East Riding, including Dame Diana Johnson, Emma Hardy, David Davis, Julian Sturdy and Rachael Maskell. It is also being supported by East Riding of Yorkshire Council, Hull City Council and the City of York Council.
Rail Minister Chris Heaton-Harris said: “For towns and villages left isolated by Beeching cuts, restoring a rail line or a station has the potential to revitalise a community.
"It breathes new life into our high streets, drives investment in businesses and housing, and opens new opportunities for work and education.
“By building back with a real focus on better connections and supporting left behind communities, we are delivering on our promise to level up this country.”