The Rail Delivery Group (RDG) said the scheme, launched on March 20, has been made “as simple as possible”.
Ukrainians are entitled to free travel across Britain’s rail network for 48 hours after arrival by showing their passport and a boarding pass or ticket with details of when they entered the UK.
The UK continues to stand with the Ukrainian people
Transport Secretary Grant Shapps
The scheme applies to all train operators.
Many train firms in other parts of Europe, as well as UK bus and coach companies, are also offering free travel.
RDG chief executive Jacqueline Starr said: “The tragedy in Ukraine has shocked us all, with people keen to offer meaningful help.
“The rail industry is proud to have been able to help play a part in making sure people affected by the tragic conflict can reach safety and comfort, and it’s fantastic to know that over 1,300 people have benefited already.
“We hope that many more people will be able to make use of this scheme and those offered by our colleagues elsewhere in the European rail family.”
Transport Secretary Grant Shapps said: “I am immensely proud of how our rail industry has come together to offer free onward travel to more than 1,300 Ukrainians, including the family who we have welcomed into our home.
“The UK continues to stand with the Ukrainian people and those fleeing Putin’s brutal invasion, and will help them to safety in any way we can.”