Labour's Paula Sherriff said one of her Dewsbury constituents pays £285 a month to travel to work near Manchester but expressed concerns over the level of compensation offered for the disruption he had experienced.
Conservative former minister Nick Herbert also said the introduction of the new timetable has been a "complete shambles" with daily cancellations of services affecting his Arundel and South Downs constituents.
He called on Commons Leader Andrea Leadsom to schedule a debate on the "abysmal performance" of Govia Thameslink Railway (GTR) and Network Rail.
It emerged today that under-fire Transport Secretary Chris Grayling is to face a protest by rail workers over the "chaos" and industrial disputes in the industry.
The Rail, Maritime and Transport union said its members will try to meet the minister at a regional transport summit in Manchester later this month.
Northern services have suffered delays and cancellations since new timetables were introduced last month, while the RMT is embroiled in a long-running dispute over the role of guards. The union has announced three more strikes for this month.
Speaking in the Commons, Ms Sherriff said of her constituent: "So far he's had to take a number of days of annual leave because of the chaos that has ensued on the rail network.
"Today he has actually been offered compensation of £20.
"I just wondered if we could have a debate in terms of what meaningful compensation actually looks like?
Mrs Leadsom expressed concern at the issue raised, adding: "That doesn't sound right to me.
"She's obviously raising a particular case and I know (Transport Secretary Chris Grayling) has proposed a special compensation scheme.
"It seems to me that she should raise this issue directly with transport ministers."
Mr Herbert also asked: "Can we have an urgent debate on the abysmal performance of Govia Thameslink Railway and Network Rail so these organisations can be held to account?"
Mrs Leadsom, in her reply, said: "The disruption to Govia Thameslink Railway services has been completely unacceptable.
"(Mr Grayling) has himself apologised for the disruption passengers are experiencing.
"(The Department for Transport) is working round the clock with GTR to stabilise the services, including monitoring ongoing performance and agreeing a revised consistent timetable."
She said she hoped Mr Herbert would encourage constituents to apply for GTR's delay repay compensation.