Office for National Statistics data shows 6,430 people were claiming out-of-work benefits as of mid-February, up from 6,020 in January.
That was the highest monthly figure since the pandemic began and more than triple the 1,950 claimants recorded a year previously.
It means 8.9% of Crawley's working-age population sought support in February – up from 2.7% 12 months earlier.
The figures include those aged 16 to 64 on Jobseeker’s Allowance and some Universal Credit claimants, who are unemployed and seeking work or employed but with low earnings.
Those on benefits last month were among roughly 302,355 across the South East.
National figures, which are adjusted to account for seasonal changes, show around 2.7 million people across the UK were seeking help in February – up from 2.6 million in January, and the highest number since comparable records began in 2008.
The ONS cautioned that changes to Universal Credit in response to the virus mean more people can get the benefits while still being employed, which could affect the figures.
It also said a small number of people who can claim both JSA and UC could be counted twice.
The Centre for Cities said the furlough scheme has helped prevent even sharper rises in the number of claimants.
Elena Magrini, senior analyst at the think tank, added: “It is already clear that the labour market today is in a much worse position than it was a year ago.
"The full extent of the damage will now depend on how quickly we will be able to exit this health crisis and on the timing of the withdrawal of the Government’s support for businesses and workers."
Separate ONS figures show the UK's jobless rate fell for the first time since the pandemic struck, despite the latest lockdown shutting large parts of the economy.
The rate of unemployment dropped to 5% in the three months to January, down from 5.1% in the previous three months, and below the 5.2% expected by economists.
The number of workers on payrolls in February also increased for the third month in a row, but there were still 693,000 fewer payrolled workers than in February 2020.
More than half of that fall was in the hospitality sector, while under-25s accounted for more than 60% of the total drop over the past year.
The Institute for Employment Studies said the labour market has started to turn the corner, with unemployment appearing to have peaked for now.
But IES director Tony Wilson added: "New hiring is continuing to fall back and all of the improvement is being driven by fewer people leaving work rather than more people getting new jobs.
"This is proving to be a disaster for young people."
Chancellor Rishi Sunak said the Government has provided £352 billion in support, and the vaccine rollout offers hope going forward.
He added: “Coronavirus has caused one of the largest labour market shocks this country has ever faced, which is why protecting, supporting and creating jobs has been my focus throughout this crisis."