Hull Trains and TransPennine Express - both owned by FirstGroup - took the longest to process their share of 3m claims following rail delays between last April and mid-October.
Hull Trains only met the one month target to process applications in 32 per cent of cases, while TpE met the target in 46 per cent of the cases, according to the regulator, the Office of Rail and Road.
In contrast Govia Thameslink Railway, which received 1m claims over the period, more than any other company, was one of 10 operators to achieve a score of 100 per cent.
The large number of claims was partly due to the chaotic implementation of new timetables in May, which resulted in severe disruption for several weeks, while Hull Trains had repeated problems with its fleet of four trains, leading to numerous cancellations.
Coun Judith Blake, Leeds council leader, who leads on transport for the West Yorkshire Combined Authority (WYCA), said: “Given the disruption to services in recent months it is no surprise passenger claims have risen sharply but it is deeply disappointing that for so many people cancellations and delays have been compounded by a protracted compensation process.
“We need to create a rail system which puts passengers first and that is what my review with the Rail Minister will address.”
Anthony Smith, chief executive of passenger watchdog Transport Focus, said in the majority of cases - 92 per cent - operators are “promptly dealing with claims” and it was “disappointing to see some dragging their heels.”
He said operators needed to take action to ensure claims were dealt with within 20 working days, adding: “The rail industry should introduce more automated compensation for delays and cancellations so that they get the money they are entitled to.”
The amount of compensation paid during disruption varies between train companies and depends on the length of delay and the type of ticket held.
Separate ORR figures show 33 complaints were made per 100,000 journeys between July and September, up 16 per cent year on year.
The punctuality and reliability of services remains the most common cause of complaints, although the overall increase was driven by a rise in frustration over train quality.
Robert Nisbet, regional director of industry body the Rail Delivery Group, said: “We know that services on some routes weren’t good enough last summer due to disruption from the May timetable change and the heatwave the country experienced.
“We want to make it simple and easy for customers to claim compensation if they’ve experienced a delay, and some train companies have introduced automatic refunds, helping claims to increase by 80 per cent over the last two years.
“As well as Delay Repay compensation, the industry has paid out additional compensation, worth up to a month’s free travel, for those on routes most affected by the timetable change.”
TransPennine Express apologised for “some processing issues” with claims last year but said they were making improvements later this year, including automatic Delay Repay, where certain customers get compensation automatically instead of having to fill a form in to apply.
A spokesperson for Hull Trains said: “In two separate periods of 2018, where our services were affected by a number of unrelated operational incidents, we experienced a backlog of claims, causing some processing delays. We apologise for any inconvenience to our customers.
“The situation is improving and we anticipate that we will be back within our customer charter target in the coming weeks - working to the same timeframes that resulted in Hull Trains consistently being ranked amongst the very best train operating companies in the UK.”
No one was available to comment from Hull Trains.