George Osborne has called on Theresa May to commit to building high-speed rail links across the north of the country.
The former chancellor said a "northern powerhouse" rail network connecting Liverpool to Hull must be planned for as the Government presses on with the delivery of HS2.
Writing in The Financial Times, Mr Osborne said: "The Northern Powerhouse Rail fits with Mrs May's stated objective of building an economy that works for everyone.
"Far be it from me to offer advice to the Prime Minister on how to relaunch her premiership this autumn, but making this big commitment to the North at the Conservative conference in Manchester would not be a bad place to start."
Mr Osborne, chairman of the Northern Powerhouse Partnership, said the body wanted a government commitment to build links across the North, starting with a line across the Pennines.
He wrote: "Northern Powerhouse Rail, or HS3, must be included in the next stage of the Government's high-speed network.
"Specifically, ministers should include the planning for the future connections when they set out the design for Phase 2b of HS2 later this year, remodelling four junctions to ensure they are complimentary with the Northern Powerhouse Rail proposals, start the detailed planning work on the line itself and allocate a long-term capital budget."
Mr Osborne said plans for HS3 "will not be cheap", with some estimates for the Pennine construction reaching £7 billion.
But he added: "This new railway would transform the northern economy."
The Prime Minister has said she remains "absolutely committed" to delivering North-South railway HS2, but has been cautious about supporting any HS3 link.
She told the Yorkshire Post in April: "The issue is there are a number of options that are being looked at in relation to HS3 or northern powerhouse rail.
"But what I would say is those big projects are not the only way in which we are looking to invest in transport in the region."
Phase 1 of HS2 is due to open in December 2026 and will see trains travel at high speed between London and Birmingham before running on from Birmingham on the existing West Coast Main Line.
A second Y-shaped phase will open in two stages.
Phase 2a from the West Midlands to Crewe will launch in 2027 and phase 2b, from Crewe to Manchester and from the West Midlands to Leeds, South Yorkshire and the East Midlands, will open in 2033.