An average of 57 trains are significantly late every day in Britain, according to industry figures.
Press Association analysis of Office of Rail and Road (ORR) data found that 5,250 trains were between 30 and 119 minutes late from July to September last year.
The Caledonian Sleeper - which runs overnight trains between London and Scotland - was the operator with the highest percentage (3.7%) of its services suffering from this level of disruption.
The second worst performance was by First Hull Trains (2.7%), followed by Virgin Trains East Coast (2.6%) and Grand Central (2%).
Passengers using Govia Thameslink Railway (GTR) - which is responsible for Thameslink, Southern and Gatwick Express services - suffered from the largest year-on-year rise in the number of significantly late trains, up 73% to 816 over the three-month period.
The figures do not include trains that were at least two hours late.
James MacColl, of the Campaign for Better Transport, urged train companies to make more effort to ensure passengers receive compensation when services are significantly delayed.
He said: "Late-running trains can be very frustrating, but far too few passengers understand when they're due compensation or how they should go about claiming it.
"With record numbers of people now relying on the railways - and technology like electronic tickets becoming more widespread - this needs to change."
Mr MacColl called for operators to make sure passengers know their rights and to ensure everyone affected by major delays gets some of their money back automatically when possible.
"With big investment going into the railways, it's also essential that the whole industry works together to minimise disruption and keep the trains running to time," he said.
The Rail, Maritime and Transport union described the statistics as "shocking" and said services are being disrupted due to "a shortage of fleet, staff and chronic under-investment in infrastructure".
The TUC claimed the data shows that rail companies believe "maximising profits is more important than delivering a good service".
A spokesman for the Rail Delivery Group, representing train operators and Network Rail, described timetables as a "promise to passengers" and insisted "we never want people to suffer delays or disruption".
He added: "Train operators and Network Rail are working hard together every day to deliver a better, more punctual railway and to give people better information when things do go wrong.
"The rail industry has cut the number of incidents causing delays every year, but a busier network means that incidents can have a greater knock-on effect."
Rail Minister Claire Perry said the compensation scheme available to passengers is "generous".