It follows a call by Transport Secretary Chris Grayling a year ago, encouraging those in the public and private sector to submit
proposals for potential projects to regenerate old lines.
The announcement will give fresh hope to dozens of campaign groups across the UK, who are still fighting to restore services cut more than half a century ago.
A spokesman for the Department for Transport told Sky News: "We are continuing to grow the rail network to deliver improvements for passengers, unlock new housing and support the economy, including by exploring opportunities to restore previously lost capacity.
"We have received a wide variety of proposals to enhance the railway from across the public and private sector, and are working with promoters to explore opportunities to re-open routes cut under Beeching.
"This is on top of exploring reopening the Northumberland Line for passenger use, supporting the reinstatement of stations on the Camp Hill Line, developing new rail links to Heathrow and a new station at Cambridge South."
The spokesman said that due to the confidentiality issues around its market-led approach, the department was not yet in a position to release details of the proposed projects, but hoped to be able to provide more information in the year ahead.
Dr Richard Beeching became arguably the most infamous name in the history of Britain's railways after he proposed almost a third of the network should be axed to try to regenerate the country's failing and unprofitable rail system.
Despite countrywide protests, by the 1970s around 6,000 miles of track had been lost and more than 2,300 stations closed.
In the years since, many campaign groups have continued their fight to have services restored and a growing number have been successful, with around 50 axed rail routes reopened.
The most successful example of a Beeching axe reversal is the Borders railway in Scotland, which largely follows the route of the old Waverley line between Edinburgh and Carlisle.
Three years ago, a 35-mile stretch of the track was reopened between Edinburgh and Tweedbank in the central Borders.
The Queen and Scotland's First Minister Nicola Sturgeon took a train journey down to the Borders to mark the return of the service.
Campaigners are now fighting to convince the Scottish and UK governments to reopen the rest of the line, through the Borders biggest town Hawick and down to Carlisle.
They point to the enormous success of the Borders railway, which has seen passenger numbers far exceed the levels predicted.
The managing director of Scotrail, which runs services on the line, is very supportive of efforts to expand the route.
Alex Hynes said: "We've demonstrated, when we build it, people will come.
"And more than three years after the opening of the Borders Railway, we have welcomed our fourth million customer onto the route.
"You might expect that three years after opening, that growth would tail off now, it hasn't.
"On the Borders railway that growth is actually accelerating which means we are going to have to operate longer trains on this route and I think there is more growth to come as well."
Mr Hynes said the restoration of the line had already impacted communities along its route in a very positive way.
"Economic studies have already shown a huge boost to tourism in the region and if you look at the amount of house building along the line of the route, the Borders railway is connecting parts of Scotland with some of the lowest economic value per head with the capital, enabling people to access jobs, opportunities, affordable housing," he said.
"It's a great economic success story for Scotland."
The rail chief has regular meetings with campaigners and others, as efforts continue to extend the line south.
"We want to see a bigger and better railway for Scotland, that will include line openings, I hope," he said.
"Ultimately it is a matter for government, depending on where the extension goes to, UK government as well.
"But we are very happy to support continuing work to look at the feasibility of extending the Borders railway further."
For the moment at least, the Borders railway terminates in the small community of Tweedbank, anyone wishing to head further south has to take the bus, car, or other means of transport.
Around 25 miles south of Tweedbank, the town of Hawick has been badly impacted in the more than 50 years since the loss of its rail service.
Before the line reopened to Tweedbank three years ago, Hawick was the furthest centre of population from a rail station on the UK mainland.
The closure of the main line through the town impacted business and saw Hawick's population shrink by more than 2,000.
Marion Short, vice-chair of the Borders Railway Campaign, regularly walks along the old railway line, heading south out of Hawick.
She told us: "The whole Borders was hit by the railway but Hawick particularly, it was a thriving industry town full of mills and the line's closure led to its demise I think.
"That was the end of it and things have gone downhill since then."
However, Ms Short said she was becoming increasingly confident that the rail line could be restored.
"We feel, based on the success we had on the first part south of Edinburgh, it has now given us the impetus to go forward," she said.
"People don't you just want the railway to come to Hawick, we want it extended through to Carlisle."
The relative success of efforts to restore long-closed rail lines comes against a backdrop of growing criticism of the state of large rail infrastructure projects like HS2 and Crossrail, billions of pounds over budget and behind schedule.
Campaigners Sky News spoke to said they felt short changed by the emphasis that is nearly always placed on rail services in the south of the country, at the expense of often vital rail links to more remote communities.
Ms Short said: "Given that everything else is behind schedule and going over budget, we think it's just a little bit of the pot that we need here.
"I think, unless you live in a rural area, people don't actually understand about the social isolation and the fact that there is no connectivity between communities.
"Speaking to ordinary individuals in this town and across the Borders, we feel somewhat cut off."
Around seven miles south of Hawick, a stretch of the old Waverley line is still running today, thanks to the efforts of a group of railway enthusiasts.
The Waverley Route Heritage Association has restored around a kilometre of track and runs several old engines on the route as a tourist attraction.
One of the heritage association's members, Bill Renwick, said he believed regenerating the old line could be relatively easily achieved.
"It's very doable, there's a tunnel not far from here where there's a small rock fall at the front," he said. "But that tunnel could be opened out, or re-lined.
"There isn't an engineering problem they couldn't get over.
"Hopefully, the Scottish and English governments, with the borderlands initiative, could make a really good case for it and get it straight across the border."
Along much of the old Waverley line, many the bridges, embankments and tunnels are still in place.
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They would all need substantial work before passenger services could run again.
But campaigners say just a fraction of the funds earmarked for the troubled Crossrail or HS2 projects would help restore rail links to some of the country's most isolated communities.