Otherwise, Mr Burnham said, Britain will be “sleepwalking toward a transport nightmare”.
Mr Burnham is pushing for Sir Keir and Chancellor Rachel Reeves to approve a blueprint for what he says will be a lower-cost alternative to the northern leg of HS2 resulting from work he commissioned with former West Midlands mayor Andy Street.
The proposal for a 50-mile Midlands-Northwest Rail Link, running from the northern end of HS2 near Lichfield, north of Birmingham, to High Legh, near Warrington, was unveiled this month.
The plan would rely on investment from the private sector and would connect the regions “at a fraction of the costs” of HS2, its backers say.
Mr Burnham said: “We have to join these dots. We’ve got a new line that the last government was committed to across the North, and we’ve got HS2 to Birmingham. That missing piece of the jigsaw has to be put in.
“You can’t have the UK’s second and third cities divided like this.”
He said he is encouraged by comments from Sir Keir last week, when the Prime Minister said that the Government would “look at” the new plan and hinted that it could be taken forward to a “feasibility study”.
Mr Burnham said that the Department for Transport also appeared to have concluded that the WCML would be full by the mid-2030s.
Mr Burnham’s warning comes after the National Audit Office said in July that scrapping of the northern leg of HS2 raised capacity issues that the Government needed to address.
Otherwise, it said, passengers would have to be put off from travelling by train once HS2 opens, most likely by raising ticket prices at peak times.