The Government has ignored calls from charities to suspend the cap, while acknowledging that the pandemic had caused a record rise in the number of households affected across Great Britain.
Department for Work and Pensions figures show 300 households had their benefits capped in Preston in May.
This was a rise of 68 per cent on the number capped in February, when there were 179 families who had either their housing benefit or Universal Credit payment reduced.
The cap limits how much households can receive in total benefits, and currently kicks in at £20,000 per year for families in Preston and most of the UK, but £23,000 for those in London.
The number of families capped across Great Britain rose to 154,000 over the period – an increase of 93 per cent.
The DWP said the rise, which was the biggest since the policy was launched in 2013, was "driven by an unprecedented increase of 665 per cent in the number of newly Universal Credit-capped households, a reflection of the impact of the Covid-19 pandemic".
The Government has decided to increase the weekly Universal Credit payment by £20 a week between April 2020 and March 2021 due to the pandemic, but Work and Pensions Secretary Therese Coffey said last month there are “no plans” to make any changes to the benefit cap system for the same duration.
Jon Sparkes, chief executive of homelessness charity Crisis, said: “These figures show thousands of people are turning to the benefits system to break their fall, only to discover that the benefit cap is cutting them off from vital support.
“If we are to avoid a wave of people from losing their homes through no fault of their own, it’s vital that the Government immediately suspends the benefit cap so that people have the means to stay afloat.
"Otherwise we risk all the good work to protect people being undone.”
Homelessness charity Shelter said many "embattled parents", already struggling from the economic effects of the pandemic, are losing vital support at the worst possible time.
Polly Neate, chief executive of Shelter, said: “The desperate calls we are getting from parents left with little to survive on – forced to choose between paying the rent or feeding their children – are a source of deep despair.
“I don’t believe this Government wants to see families left hungry, hopeless and facing homelessness while this deadly virus continues, but this is what is happening.
“We are in extraordinarily difficult times, this flaw in the welfare system has to be fixed before a flood of families find themselves destitute."
Of those now affected by the cap in Preston, 68 per cent (203) are single parents – compared to 62 per cent across Britain.
A DWP spokesman said: “The benefit cap ensures fairness for hard-working taxpaying households and a strong work incentive whilst providing a much-needed safety net of support.
“We remain committed to helping the most vulnerable in society, which is why we currently spend more than £95 billion a year on the benefits system, supporting more than 7m people.”