The two councils have agreed to work on a study that examines the economic connections between the cities and with a number of the English cities that stand to benefit from high-speed rail.
Councillor Tom Buchanan, the city's economic development leader, said: "Glasgow and Edinburgh probably have many more people using planes to go to London than the other English cities.
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Hide Ad"When we have high-speed rail, people will be able to get to London in three-and-a-half hours, which will make a big difference."
The study will look at the benefits of high-speed rail, the costs of infrastructure involved and how to bring groups together to work on the case.