Figures obtained by Labour MP Jim McMahon through a parliamentary question, and reported by ITV, show that 1.3 million calls were abandoned between September 2016 and October last year.
The shadow minister for communities and local government warned the number of calls going without an answer could mean many claimants were giving up trying to get through and not getting the support they need.
However, the Department for Work and Pensions (DWP) called these claims “disingenuous”, saying calls were answered on average within five minutes.
But Mr McMahon said that staff were struggling to cope with the volume of calls and that claimants had to wait for lengthy periods of time to get assistance.
The figures showed that more than 120,000 calls were abandoned each month in August, September and October, the highest numbers over that period.
Calls to the Universal Credit helpline were answered within five minutes on average in December.
“Everything we hear about Universal Credit suggests that it is failing in its purpose to provide help and support to vulnerable and low income claimants,” Mr McMahon said.
“I worry that at this busy time of year, people needing help to make ends meet – many of whom are hardworking people – won’t get the support they need from the government.”
Charges for the helpline were scrapped last year after it was revealed that people could be paying up to 55p a minute for calls to fix problems with their claim.
The DWP said that 95% of Universal Credit claims are now online, with more than 80% also reporting any changes to their claim digitally.
Mr McMahon said there was no evidence to suggest that those abandoning calls were moving online.
“DWP have made a very broad assumption that abandoned calls are due to claimants moving online,” he said.
“It raises a big question about how much of a handle the DWP have on the experience of their customers.”
A DWP spokeswoman said: “These claims are disingenuous – there are a number of reasons why someone might end their call, and calls to our Universal Credit service lines are being answered within five minutes.”