A survey of 32 key organisations showed that nearly 90% saw building a line north of Manchester and Leeds, which are due to have a high-speed rail connection to London by 2033, as important or very important.
A key driver is the belief that the East and West Coast Main Lines will be full by 2030, putting a strain on train journeys to Scotland.
The findings, due to be published today by high- speed lobby group Greengauge 21, provide a welcome boost for the Scottish Government's ambitions to be included in a UK network of new rail lines capable of carrying 250mph trains and follow Alex Salmond's calls for a "northern accord" to be forged between Scotland and the north of England.
Infrastructure Secretary Nicola Sturgeon announced plans earlier this week to push ahead with a new high-speed line connecting Glasgow and Edinburgh.
Jim Steer, an influential transport expert who founded Greengauge 21 in 2006 to push the case for high-speed rail, said a key question now emerging was how to bridge the "northern gap" between the planned high-speed network in England and the Scottish border.
The involvement of councils and transport authorities could be an important factor in this as they could have a role in deciding whether a high speed rail route is funded.