The trust has submitted a detailed plan to the Department for Transport, outlining the proposals in a request for money to further develop the ideas.
The plan would create a 10-mile route, with six new stations, and ambitions to link with the Severn Valley Railway in Bridgnorth.
It could also connect to Telford, if plans from Telford Steam Railway to extend its line are developed.
Councillor Eric Carter, chairman of The Marches Strategic Railway Group, said the bid offered huge potential benefits for green travel and the county economy.
He said: “It is a once-in-a-lifetime opportunity – and just think of the benefits it would bring to the Ironbridge Museum, there is potential for getting people down from London on the line. It is an ideal development for the future.
“We have had talks with shopkeepers in town who see the benefits, it would be great for the area generally, there are so many opportunities. We can’t afford to miss this. We do not want to see the line taken up.”
Councillor Carter said the bid had a number of advantages over rivals – most importantly that the majority of the rail line is still in place.
He said: “If we don’t have the vision it does not happen. We have seen so many times in the past where lines have been built over and misused, and later on you think it would be great to get back there and you can’t because there is a housing estate on it. So you have to have the vision now and that’ what I am determined to do.”
The proposal puts forward ideas for creating stations at Ironbridge Parkway, Ironbridge & Broseley – for the Iron Bridge, Jackfield – for the Tile Museum, Blists Hill, Coalport – for the China Museum, and Linley – for Apley Hall.
The bid outlines plans for a timetable of four trains per hour – one going from ‘Ironbridge Parkway’ to Ironbridge, then Coalport, Bridgnorth, and potentially on to Kidderminster, and another three from ‘Ironbridge Parkway’, stopping at Ironbridge and Coalport.
The Ironbridge Parkway site would be created to link the planned development at the former power station, where site owners Harworth want to build up to 1,000 homes in what will effectively be a new community.
The proposal for the rail line has received the backing of Telford MP Lucy Allan and Shrewsbury and Atcham MP Daniel Kawczynski – as well as Wyre Forest MP Mark Garnier.