Network Rail said limited trains will operate overnight from Wednesday night while Her Majesty is lying in state in Westminster Hall. There will also be extra daytime services.
Avanti West Coast said it is running up to four additional services a day in each direction between London, the West Midlands and Manchester from Tuesday up to and including Friday, adding a total of around 16,000 seats to its capacity.
The company said it is "examining closely what opportunities there are for additional services" on Saturday and Sunday and that transport plans for the day of the funeral are still being finalised.
It has operated a reduced timetable in recent weeks due to drivers refusing to work overtime shifts.
It is understood around 200 daily services will be added to timetables nationally. They will be displayed on online journey planners.
A Network Rail spokesman said: "The rail industry is doing all it can to ensure people can travel to pay their respects during the period of mourning.
"Where possible, we will be running some extra services, including a very limited service operating through the night on some routes, and postponing engineering work.
"Customers should check journey planners for the most up-to-date information."
A rail industry source said the limited number of overnight services means they are "not something people should be relying on".