Between April and September, the trust says, there was a 30% increase in demand for food banks in areas where full Universal Credit had been in place for six months or more, compared with the same period in 2016.
Despite faster advance payments now available to people claiming the benefit, the charity is warning that the changes will not be enough for some.
"With long waits for payments and some poor administration, we're concerned that even more people will be needing food over Christmas," said Mark Ward from the Trussell Trust.
"Though we welcomed changes to Universal Credit announced in the Budget, many improvements will not come into force until 2018, and do not go far enough to fix all of the problems with the new system."
The Department for Work and Pensions rejected the criticism. "Anyone applying for Universal Credit has access to advance payments within five working days, and on the same day in urgent need," said a spokesperson.
"Work is the best means of providing people with financial security, and with our welfare reforms people are moving into employment faster and staying there longer."
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