The mayors of Greater Manchester and the Liverpool city region have demanded a freeze in rail fares after months of travel chaos across the country.

In a joint letter to the transport secretary, Chris Grayling, the mayors Andy Burnham and Steve Rotherham said the anticipated 3.5% rise in fares would “add insult to injury” for beleaguered passengers.

The annual cost of getting to work for many long-distance travellers is expected to rise by more than £150 next year.

The exact increase will be confirmed when the July retail prices index (RPI) measure of inflation is released by the Office for National Statistics on Wednesday, but economists from Investec and the EY Item Club both predict the figure will be announced as 3.5%.

More than 9,000 Northern rail services have been cut from the schedules over the past two months after the introduction of a new timetable, which also caused disruption on various London commuter lines. Thousands of passengers are still waiting to receive enhanced compensation.

The disruption led to the government vetoing further timetable changes expected in December, which means upgrades in areas such as the West Midlands, the west of England and along South Western Railway routes have been cancelled or delayed indefinitely.

In their letter to Grayling, Burnham and Rotherham said the disruption had caused “real damage” to the north of England economy.

Analysis from the Northern Powerhouse Partnership (NPP), a thinktank set up by the former chancellor George Osborne, found £38m had been lost to the northern English economy on Northern trains alone this summer, and up to £1.3m a day at the height of the crisis.

“The rail industry has caused real misery for thousands of passengers across the north,” the Labour mayors said. “Not only have people lost time at work or with their families, they have had to shell out for taxis, extra childcare and even hotel bills because of the continuing disruption.

“To ask these long-suffering passengers now to pay even more for a poor, unreliable service is to add insult to injury. A freeze in the current fares is the very least that passengers deserve.”