Railway lines closed in the 1960s could be reopened if they boost the economy, the government has said.
The plan forms part of a wider rail strategy under which the government will consider splitting up two of the biggest train operators.
The move would affect Great Western and GTR, which comprises Southern, Thameslink and Great Northern.
The government also plans to devolve running the track and train services to local companies.
At the moment Network Rail, which is state-owned, looks after the track and other infrastructure while train services are operated by private companies.
The first public-private partnerships introduced would be on the East Coast mainline from 2020, which connects London, the North East and Scotland.
Mr Grayling described Network Rail as “one big central blob”, saying the network could be better run locally.
“It means when things go wrong, there’s one team to sort it out,” he told BBC Radio 4’s Today programme.
Some 4,000 miles of rail routes were closed in the 1960s, mainly in rural areas, known as the Beeching cuts.
Transport Secretary Chris Grayling said the new rail lines could unlock jobs, encourage house building and ease overcrowding.
“The system is creaking – it’s bursting at the seams,” he said.
Mr Grayling said the new routes would “provide better services for commuters but also unlock housing potential”.
Work on the Oxford to Cambridge route starts next summer, and plans to re-open routes around Bristol, Birmingham, Exeter and the North East are being considered.
The government will also consult on splitting up the Great Western franchise between London, the South West and Wales.
That could result in one company running long-distance lines between London, Wiltshire, Somerset, Devon and Cornwall – while another runs local services across the South West.
Train and track together?
By BBC Transport Correspondent Richard Westcott:
I have never met anyone in the rail industry – either pro- or anti-privatisation – who thinks it was a good idea to split up who runs the trains and who runs the track and signals.
But that is what we have got.
Since the 1990s, there have been plenty of stories about Network Rail teams arguing with train company teams about who should fix a problem and who should pay – causing plenty of unnecessary delays.
Now, the government has said it will change things to create joint teams – with one boss, public and private working together, to solve problems on the line.
The biggest experiment will be on the East Coast mainline, where Virgin-Stagecoach is struggling to make money and has become frustrated with the physical state of the line.
A new public-private partnership is being set up to run the train and tracks together.
But we have no idea yet how it will work, who will pay for things, or when passengers might feel the benefit.
But Labour has called the ideas “un-funded proposals”, with shadow transport secretary Andy McDonald describing the plans as “unambitious”.
“The Tories’ record is of delayed, downgraded and cancelled investment, huge disparities in regional transport spending and soaring fares that are pricing passengers off the railway,” he said.
Mick Cash, general secretary of the RMT union, said it was a “scandal” that the plans did not consider publicly-owned railways.
He said: “The planned breaking up of Great Western and GTR is a massive admission of failure by the government but still they rule out the highly popular option of public ownership.”
Mick Whelan, general secretary of the train drivers’ union Aslef, said the union would be “pleased to see the lines cut by Beeching restored”.
However, he said Mr Grayling’s new plans would not boost jobs and housing, asking:
“Where is the bold strategic vision for rail – and integrated transport links – in this country?”
Councils and business have also been asked to submit proposals for new lines.
However, the government has no plans to make new money available to fund any such suggestions, the BBC’s transport correspondent Richard Westcott said.
Who was Dr Beeching?
Richard Beeching’s brief as chairman of the British Transport Commission was simple: “Make the railways pay.”
British Rail was losing £140m a year when Dr Beeching took over the commission. His solution, announced on 27 March 1963, was equally straightforward – massive cuts.
The Conservative government welcomed the report, but thousands of people – many in remote rural areas – were horrified they would lose their local branch lines.
Opposition from the pressure groups failed and during the 1960s “Beeching’s Axe” fell on 2,128 stations and more than 67,000 British Rail jobs.