Thirty-one MPs, 20 business organisations, 11 council leaders and three university vice chancellors have signed the letter to the transport secretary and chief secretary to the treasury.
In it, they call for Network Rail to be given money to start drawing up detailed plans for the work.
“These schemes have been in the pipeline for decades with the case for them strengthening year on year.
“They are now restricting growth and the country’s progress to cleaner, greener transport connections,” the letter says.
Rail lines from the Midlands, Cambridge, Kings Lynn, Norwich and Ipswich all meet at Ely, while Haughley, which lies to the north of Stowmarket, needs to be enlarged to accommodate the busy freight route from Felixstowe and the intercity service between Norwich and London.
The letter says improving the junctions would allow 2,900 extra freight services to run between Felixstowe and the Midlands and remove the need for 98,000 HGV journeys every year.
The work would also relieve pressure on the local road network and encourage the building of new homes along the various routes which pass through the two junctions.
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