It has lifted ticket restrictions to enable customers to travel before the chaos hits on Sunday over “a number of factors” – including the football match between France and Croatia.
The reduced number of staff on Sunday has also been blamed on “continuing good weather and the start of the school holidays,” according to a statement from GWR.
Passengers are advised to travel as early as possible and to even consider switching their travel plans to alternate days.
Long distance services including routes between Paddington and Bristol, South Wales, Oxford and Devon and Cornwall will be most affected.
Trains that will be running are expected to be extremely busy, and there will be some changes to suburban services in the West.
GWR Managing Director Mark Hopwood said: “We will have managers and volunteers throughout our network to help at stations and on board, but unfortunately we will not be able to deliver our planned timetable of services; and the trains we are able to operate will be extremely busy.
“I would encourage customers to travel on a different day if they are able to and we will happily offer refunds to those who choose not to travel.
“We are very sorry for the inconvenience this disruption will cause.”
Full details of the revised timetable are now available online.
Those who choose not to travel will be entitled to a full refund on their unused ticket.