Westminster Scottish secretary David Mundell has confirmed that ministers south of the border want to see such a study carried out as part of the £345m Borderlands growth deal announced last month.
Hopes are high that heads of terms for that deal will be signed off in June, so, if the Scottish Government and five councils also involved in the initiative agree, work on a study could begin within months.
That news has been welcomed by the Campaign for Borders Rail and MPs and MSPs.
Campaign chairman Simon Walton said: “This is really good news.
Elliot's ‘surreal’ week capped by special responsibility
Artists open their doors to the public at Marchmont
Two Borders pubs named best in Scotland for beer and food
Souters help us solve mystery of old photo taken in Selkirk
In pictures: 12 of the best pubs in the Borders, according to the latest Good Beer Guide and Good Pub Guide
“The campaign has worked closely with elected representatives over the years to promote the benefits of reestablishing a direct rail link through the Borders, connecting both north and south with the national network.
“We’re delighted with this progress, confirming the secretary of state’s support for a feasibility study into extension of the Borders Railway through Hawick and onwards to Carlisle.
“The positive benefits would contribute to the economic development and regeneration of the whole area, both in terms of passengers and freight, and also support a growing tourism industry.
“It is hoped that this will ensure greater connectivity of all communities and be a positive move towards social inclusion.
“With the help of the community at large, the campaign continues to work with Westminster and Holyrood governments to make this a reality.”
Dumfriesshire, Clydesdale and Tweeddale MP Mr Mundell’s pledge of support was made in response to Berwickshire, Roxburgh and Selkirk MP John Lamont raising the issue at prime minister’s questions in the House of Commons last Wednesday.
Treasury minister Mel Stride told him the Department for Transport is supportive of a feasibility study, and Mr Mundell has since confirmed that the UK Government would like to see it funded out of the £260m it announced for the Borderlands deal last month, supplemented by £85m pledged by Holyrood ministers.
Mr Lamont has welcomed that commitment, saying: “This is great news for the campaign to bring the Borders Railway to Hawick and beyond.
“We need to improve transport links across the whole of the Borders, and extending the Borders Railway is part of this.
“A full feasibility study will look in detail at the costs and benefits of bringing the railway to Hawick, Newcastleton and on to Carlisle.
“I’d expect this to look at things like impact on businesses, jobs and tourism as well as the implications of getting freight off our roads.”
The Borders’ two constituency MSPs, Rachael Hamilton and Christine Grahame, are equally pleased to see moves to extend the 30-mile Edinburgh-Tweedbank track building up a head of steam.
Ettrick, Roxburgh and Berwickshire MSP Mrs Hamilton said: “I welcome the commitment from the UK Government to look into a full feasibility study. The extension is vitally important to cross-border travel.
“The Borderlands deal provides some much-needed investment for infrastructure, and I hope this will attract more businesses investment into the area as a result.”
Midlothian South, Tweeddale and Lauderdale MSP Christine Grahame MSP said: “The Borders Railway has been a fantastic success, boosting the economy, leading to new housebuilding and supporting tourism in the region.
“My constituents will significantly benefit from any welcome extension to the existing Borders Railway, and I am sure they will welcome the news of a feasibility study into the benefits of extending the railway to Hawick, Newcastleton and Carlisle.”
A Transport Scotland spokesperson added: “We understand the importance of connectivity in the area and have already completed pre-appraisal work through the Borders transport corridors study.
“This identified the option of extending the Borders Railway to Carlisle as one of 21 potential transport interventions for further consideration through our strategic transport projects review.
“We welcome the opportunity to discuss potential joint funding for a detailed consideration of cross-borders transport links that would align with the outcomes of the second strategic transport projects review, once it is completed.”
Extending the £353m line, opened in September 2015, to Hawick, via Melrose, would add about 17 miles to its current 30-mile length, and carrying on to Carlisle, via Newcastleton, recreating the old Waverley Route closed in 1969, would require another 50-plus miles of track on top of that.