Northern suffered an increase in the rate of complaints of 63 per cent and TransPennine Express (TPE) a 21 per cent rise between April and June, compared with the same period last year, Office of Rail and Road (ORR) data shows.
Northern had services crippled on many routes when new timetables were introduced on May 20, with the number of daily trains cancelled reaching 310.
There was also a knock-on effect which caused widespread problems for TPE.
Labour said the level of complaints showed that rail privatisation had failed and called for a freeze in fares.
The timetable changes were intended to deliver huge benefits to passengers as a result of major upgrades to the network.
The ORR, which is investigating the chaos, published an interim report last month that warned of a "lack of clarity about roles and responsibilities" and said "nobody took charge".
Northern and TPE were among 13 train operators that had their complaints rate rise between April and June.
Other firms to suffer an increase include London and North Eastern Railway (up seven per cent), Govia Thameslink (up 23 per cent), CrossCountry (up 40 per cent), Great Western Railway (up 80 per cent) and Heathrow Express (up 60 per cent).
The average rate of complaints across all operators was 29.9 per cent per 100,000 journeys, representing a 6.6 per cent year-on-year increase.
The most common complaint category was punctuality/reliability at 22 per cent of all complaints, up 1.3 percentage points compared with the same period last year.
Shadow Transport Secretary Andy McDonald said: “With delays and cancellations rising, it’s no wonder complaints on the railway have soared.
“It’s clear that privatisation has failed and that the Government is incapable of delivering reliable and affordable rail services. Worse still, Chris Grayling’s officials are protecting private profits at the expense of commuters by attempting to prevent them from claiming the compensation they are owed.
“The train companies responsible for the timetable disruption must be made to freeze fares next year. Ultimately, to put an end to failing and unaffordable rail services, the railway should be brought into public ownership, a policy that is backed by two thirds of the public.”
Robert Nisbet, regional director of the Rail Delivery Group which represents the railway, said: “All of us who work in the industry know we have to work hard to build trust with passengers after a difficult summer mainly due to the May timetable.
“We’re delivering a plan to improve and change - look at the new ombudsman service we’re launching, which will give passengers a fair hearing when things go wrong.
“We are also investing record amounts in trains, as we roll out new carriages and services across the country so people will soon see improvements to their journeys.”
A spokesman for Northern said: “Following the collapse of Carillion, which had previously handled our complaints, we rapidly had to bring all customer service functions in-house. The transition resulted in a short term reduction in our ability to process complaints as quickly as we would have liked. We are sorry for the impact this had on our customers.
“During April, May and June our customers faced unprecedented disruption as a result of delayed infrastructure delivery and the resulting timetable problems which led to an increase in complaints and compensation claims. This increase put further pressure on the customer service team which is now working at full speed to respond to outstanding complaints and clear any remaining backlog.”