The additional services will further boost passenger numbers, which are already at an all-time high of 1.73 billion journeys a year - twice as many as in the 1990s.
They will include ScotRail’s biggest increase in trains for 25 years, announced last year, thanks to two new fleets.
A further 200 services will be added to its current 2,300 a day in 2018 and 2019.
They include on a fifth route between Edinburgh and Glasgow, via Cumbernauld.
Additional stopping services on routes such as Edinburgh/Glasgow-Aberdeen will supplement limited-stop trains.
There will also be more cross-Border trains run by Virgin Trains East Coast and TransPennine Express - also using new fleets.
They include TransPennine’s new Liverpool to Edinburgh and Glasgow services via the east and west coast main lines.
A new low-fare Edinburgh-London service by former ScotRail operator FirstGroup will be launched in 2021.
In London, 805 trains a day will run on the Elizabeth line - the east-west CrossRail route - when it is fully opened in 2019.
The Rail Delivery Group, representing train operators and track owner Network Rail, which published the research, said more trains were vital to meet rising demand.
Chief executive Paul Plummer said: “Rail is an ever more vital public service, enabling jobs, housing and economic growth. But there’s a capacity crunch affecting the railway, with journeys having doubled in 20 years and the number of trains increasing too.
“That’s why we’re delivering billions of pounds of improvements and reversing decades of under-investment.
“The £50 billion-plus Railway Upgrade Plan will help ease the congestion.
“It will break bottlenecks, untangle tracks and harness technology so that more trains can run to more places more often, creating new opportunities and supporting jobs.”
Lianna Etkind, of the Campaign for Better Transport, said the increase in trains would “ease the overcrowding which makes so many commuters’ lives a misery”.
But she also called for investment in longer trains, and for smaller towns and villages to be better connected with public transport to ensure rail offers a “viable and environmentally responsible alternative to car travel”.