The Public Accounts Committee said the total UK tax debt was £39bn – more than double the amount at the start of 2020.
It said HM Revenue and Customs must pursue businesses and individuals who were choosing not to pay their taxes while supporting those still struggling with the impact of the pandemic.
HMRC said it was recouping debts and would also be recruiting more staff.
After the UK first entered lockdown, HMRC paused most debt collection activity, significantly reducing the number of letters sent and in-person collections conducted.
The move, along with the wider economic impact of the pandemic, saw the number of taxpayers in debt rise from about 3.8 million in January 2020 to 6.2 million in September 2021.
The total amount owed rose from about £16bn before the pandemic to a peak of £67bn in August 2020, before falling back down to current levels.
The Public Accounts Committee’s report said HMRC had not “articulated a clear plan or set out a detailed timescale to give us confidence it can manage the challenge it now faces”.
The cross-party committee added that the longer the tax went unpaid, the greater the risk that HMRC would never be able to collect it.
It was particularly concerned about “rogue firms” that have been able to profit by exploiting measures put in place as part of the pandemic response.
The report also expressed concern that HMRC was not being proactive enough in identifying and offering support to people who had been left economically vulnerable or less able to pay their debts because of the pandemic.
Committee chairman Dame Meg Hillier MP said: “HMRC has a tricky balance to strike. Those least able to afford rising bills, including tax bills, are also the easiest collection ‘targets’.
“At the same time, HMRC’s challenges chasing down high-wealth individuals and companies who take advantage of every trick in the book to avoid and evade tax and outrun the law are well-known.
“Those tricks are just not available to ordinary people, now emerging from the misery of the pandemic into an exploding cost of living crisis. HMRC must push much harder at the doors – no matter where they are – of those who are not paying their fair share.”
In a statement, HMRC said: “We are recouping debt safely, taking into account customers’ circumstances and making repayments affordable. It’s in no-one’s interests to push viable businesses into insolvency when they can succeed given some time to repay their tax debts.”
It also said it would be recruiting almost 2,000 extra staff over the next year to support collection efforts.