Some 152,154 people received three days' worth of emergency food between April 1 and June 30, up from 49,596 last year.
The charity said 52% of people were referred to the foodbanks by care professionals as a result of benefits problems, up from 43% in the same period in 2012.
Of those referrals, 19% were due to changes in the benefits people were entitled to and 33% were due to delays in payments.
Trussell Trust executive chairman Chris Mould said: "The reality is that there is a clear link between benefit delays or changes and people turning to foodbanks, and that the situation has got worse in the last three months.
"Since April's welfare reforms we've seen more people referred to foodbanks because of benefit delays or changes.
"Our foodbanks are reporting that many local authorities and agencies are unclear about what help is available to individuals who would previously have been helped by the social fund and are consequently giving poor or inappropriate advice to people.
"We're also seeing more people turning to us who have been sanctioned for seemingly illogical reasons and we're helping people who cannot afford the bedroom tax but are unable to move house."
Mr Mould called for the Government to take action before the introduction of the universal credit begins in October. He said: "We are calling on the Government to listen to what's happening on the ground, to realise that when the welfare system breaks down, it means families go hungry."