Research by Citizens Advice found that more than a third of those helped by the charity found it difficult to provide evidence on issues such as health, housing and childcare, to complete their claim.
It was also revealed that people who received their first full payment late stood a higher chance of falling into debt.
Citizens Advice said people must wait five weeks before receiving their first Universal Credit payment, so their finances are often already stretched.
The charity called on the Government to simplify the claims process and urgently put improvements in place as roll-out of the benefit continues.
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Gillian Guy, chief executive of Citizens Advice, said: "While Universal Credit is working for the majority of people, our evidence shows a significant minority are struggling to navigate the system.
"With people already having to wait five weeks as a matter of course for their first payment, any further delays risk jeopardising people's financial security.
"Last year the Government showed it was listening by taking important steps to improve Universal Credit.
"Those measures are starting to have an impact, but more needs to be done.
"Top of the Government's list should be simplifying the process and making sure adequate support is in place so that claims can be completed as quickly as possible."
A Department for Work and Pensions spokeswoman said: "Universal Credit simplifies an out-of-date, complex system, and we welcome Citizens Advice finding that it is working well for the majority of claimants.
"We continue to listen to feedback and make any necessary improvements during the roll-out with our 'test and learn' approach, and this report recognises the positive impact of changes we have already made.
"The vast majority of Universal Credit claimants are paid in full and on time, and 100% advance payments can be made available within hours. We also fast-track appointments for customers in need.
"We look forward to working collaboratively with Citizens Advice and others to ensure that the small minority who seek additional help making their claim are able to access it."
Margaret Greenwood, Shadow Work and Pensions Secretary, added: "This report adds to the evidence from the National Audit Office and DWP itself of just how difficult many people find making a claim for Universal Credit as they struggle to navigate the online system.
"The Government should have got something so basic as verifying claimants' identities and evidence right from the beginning, rather than leaving people facing long delays for payments which can often lead to debt.
"The Government must pause the roll out of Universal Credit and fix the problems so that no more people are pushed into poverty by the major flaws in its design and delivery."
It has also been claimed that so many faults have been designed in to the Universal Credit system, including wrongly reducing benefit by hundreds of pounds, that it is bound to trigger harmful mistakes and delays.
The allegation is made by an unnamed service centre worker who told The Guardian: "The IT system on which universal credit is built is so fundamentally broken and poorly designed that it guarantees severe problems with claims."
The whistleblower added: "In practical terms, it is not working the way it was intended and it is having an actively harmful effect on a huge number of claimants."
A DWP spokesman said: "Universal credit is a flexible and responsive benefit and we continue to listen to feedback and make any necessary improvements during the rollout with our test-and-learn approach.
"We are committed to ensuring people get the help they need and the majority of staff say universal credit gives them greater flexibility to give people the right support. The latest figures show 83% of claimants are satisfied with the system and complaint rates are low."