Under the policy the journey from London to Edinburgh and Glasgow would be cut to two and a half hours hours – down from four today – likely eliminating the need for vast numbers of domestic flights and slashing CO2 emissions.
The opposition's commitment to the delayed mega-project comes after Boris Johnson threw its future into doubt by launching a review of whether it should go ahead or not.
The Scotland extension of HS2 is one of a number of rail projects backed by the opposition party in the section of its manifesto pledging a "green industrial revolution": with plans to overhaul transport and energy systems across the country.
The manifesto also commits the party to a new east-west rail line across the North of England dubbed "Crossrail for the North", and rail electrification of existing lines plus their expansion "across the whole country".
A Labour government would also start a rolling programme of rail electrification, "to ensure continuity of skills, jobs and supply chain capacity to reduce costs" – a proposal that has strong support in the rail industry.
Several rail electrification projects were halted or pared back by the last transport secretary Chris Grayling because of rising costs, including the South Wales mainline, the Midland mainline, and in the Lake District.
The investment pledges come as Labour pledges to take railway services back into public ownership, creating an organisation which "will steer network planning and investments" as well as "co-ordinate mainline upgrades, resignalling, rolling stock replacement and major projects".
A leaked report of Boris Johnson's so-called Oakervee Review into HS2 revealed at the start of the month recommended the project should go ahead, though its official release has now been put back to the general election – effectively parking the issue until the next parliament.
The project has been beset by rising costs and delays, and critics say it is too expensive. Its advocates argue that it is needed to provide rail capacity between cities and improve local inter-urban services as well as reduce journey times.
The current plan for the rail line runs from London to Manchester and Leeds in a Y shape via Birmingham, the East Midlands, and Crewe. High-speed services would also call at other many cities such as Sheffield, Stoke, Edinburgh, Glasgow, and Newcastle by using existing lines to continue their journey.
In addition, the line would boost local services serving smaller towns by taking fast services off existing lines and leaving more space for slower inter-urban and regional trains.
There are no details about the route HS2 would take to Scotland in Labour's manifesto, but the party says it would take "full account of the environmental impacts of different route options". The commitment to extend the line to Scotland was also included in the 2017 manifesto, before this year's review was launched.
A broad options report released by the Government in 2016 found that 200km of new lines would be the best way of getting London–Scotland central belt journey times down to under three hours, with upgrading existing lines likely to "deliver limited journey time saving (less than 15 minutes) have high cost, and potentially impact capacity".
By contrast, new high-speed track could either go up the east or east sides of the country, starting from the current planned ends of the railway line.
"This approach could achieve a journey time in the order of 2 hours 30 minutes from London Euston, saving over an hour on the substantial improvement already made with Phase Two," the DfT said.
"Depending on route and intermediate station provision, it could offer similarly significant savings to journeys between Scotland, the North of England and other cities in the UK."
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