While families of all sizes have been affected, single parents, couples with a single earner and large families have been hit the hardest.
The report, No Longer Managing, identified four factors behind the growth in poverty: spiralling housing costs among low-income households, low wages, an inadequate social security system and a lack of flexible and affordable childcare.
Two-earner families, where one partner works full-time and one works part-time, were found to be most at risk of in-work poverty.
For people in this group, the chances of being pulled into poverty have doubled over the past two decades, from one in 20 to one in 10.
Even for households with two people in full-time work, the chances of being pulled into poverty have more than doubled over the same period, rising from 1.4% to 3.9%.
Couple households with one full-time earner now have also have a poverty rate of 31%, almost as high as working households where nobody works full time.
Clare McNeil, IPPR associate director and head of its Future Welfare State programme, told HR magazine the rise in working poverty cannot be solved by government alone.
She said: “There are a number of things employers can do, from increasing flexible working options for parents to allow them to work around childcare commitments and advertising jobs on a flexible basis, to using fixed contracts with regular hours in favour of insecure or temporary contracts.
“Equally important is investing in employee skills to give them the best possible chance of progressing out of low pay.”
The IPPR said the government’s current levelling-up agenda is unlikely to benefit working families if it remains largely focused on physical infrastructure and fails to address growing inequalities.
These include rapidly rising house prices and the growing gulf between property owners and renters.
The think tank recommended labour market reforms, an effective skills policy and more income support.
McNeil said an alternative to levelling up is needed, "something that looks beyond headline incomes to the true costs and obstacles people face when struggling to make work pay".
She said: “If this does not happen, more and more families who were once just about managing will join the growing number who are no longer managing.
“Short-term fixes are needed to alleviate the immediate crisis, but to solve the underlying problem we need a far deeper rethink of housing, childcare, social security and work.”
The dangers of in-work poverty: