Consumer groups have urged all rail operators to follow Virgin Trains' decision to offer compensation in the form of a cheque as the default option rather than travel vouchers.
The policy will apply on Virgin's east and west coast routes.
Anthony Smith, chief executive at the independent watchdog Transport Focus, said: "Passengers will be pleased to see Virgin Trains offering cash compensation as the first option. This is a positive step forward and we want to see more operators follow suit."
He added that many people are not claiming the compensation they are entitled to.
Richard Lloyd, executive director of consumer group Which?, claimed passengers are "rightly frustrated by the significant barriers" to obtaining compensation.
"It is good to see Virgin Trains setting the pace by offering cash as the default option for compensation," he said.
"We would urge all train operating companies to act quickly to implement this, and further changes, to improve the process for their customers."
The announcement is the latest attempt by Virgin Trains to improve its response to disrupted journeys.
In October the firm launched a system whereby west coast travellers who buy Advance tickets through its website receive money directly on to their payment cards if they are entitled to compensation.
Virgin Trains issued a statement which claimed "we always want to be on the side of passengers".
New arrangements came into effect in July last year meaning all rail passengers can request to receive their payout in cash.
Some 5% of services run by Virgin Trains were either cancelled, at least 30 minutes late or missed a scheduled stop in the 12 months to March 5, according to Network Rail figures.
The average for rail firms across England and Wales is 3%.
Graham Leech, group commercial director at Virgin Trains, said: "We're committed to making claiming compensation simpler and clearer for customers.
"We never want passengers to suffer delays or disruption but when things do go wrong we want to put it right."
Virgin Trains was one of the operators affected when damage to overhead electric wires near Birmingham Airport caused severe disruption on Tuesday.
The problem affected routes serving much of the country, including Edinburgh, North Wales, Manchester, London and Southampton.