Govia Thameslink Railway, which also runs Southern, Gatwick Express and Great Northern rail brands, has faced heavy criticism for its performance since new timetables were introduced last week.
The company has apologised to passengers and has introduced a reduced timetable for Great Northern and Thameslink networks.
More than 7,000 people have signed a petition calling for GTR to have its contract removed immediately.
And the situation was not improved when Thameslink’s Twitter account described how its services are ‘less Ferrero Rocher and more Poundland cooking chocolate’ on Wednesday.
Austin Cooke, Poundland’s retail director, said in response: “We couldn’t help but notice that your Twitter team described your failure to provide an adequate service as ‘Poundland’ cooking chocolate.
“Aside from the breach of our trademark, we think you’re taking the biscuit.”
He added: “Frankly you have no right to use our name to describe poor service. We served eight million shoppers last week and didn’t have to close any store due to leaves on the roof, the wrong kind of rain, or a shortage of managers.
“In fact, our Welshpool store flooded and our store colleagues stood at the entrance to help customers get their shopping, so we stayed open.
“We think we have a pretty good idea about what great customer service is compared to most rail companies.
“But if we ever fall short, perhaps we’ll describe ourselves as a bit Thameslink.”
Thameslink then apologised for using Poundland’s name and deleted the original tweet.
Earlier this week GTR apologised to passengers for the continued disruption linked to the introduction of the new timetable.
In a statement on its website GTR said: “We are working on a recovery plan with rail industry partners.
“Meanwhile, as late notice changes continue to be made, we ask passengers to check train times on the day of travel using our service updates page. We expect disruption to ease over the coming month.”
In a letter to MPs, Transport Secretary Chris Grayling criticised the ‘wholly unsatisfactory levels of disruption on rail services following the huge timetable change last week’.
He said: “I am frustrated that what should have been a good news story for passengers, with the introduction of new services, new routes and expanded capacity has had such a poor start.
“The industry collectively has failed passengers.”
He added: “We were aware that there might be some disruption in the early days of any new timetable change of this size, but the scale of the problem has far outstripped any expectation.
“I am determined both that the problems are dealt with as quickly as possible, and that this is not repeated in the future.”
Peter Kyle, Labour MP for Hove, said: “It’s grotesque of Chris Grayling not to accept any responsibility for the timetable disaster.
“If he doesn’t know that his department sets most of the timetable, collects the fares and had sign off over the reforms, and still thinks he couldn’t have done better, he should be sacked.”