The Public Accounts Committee was particularly scathing of the taxman, saying HM Revenue & Customs (HMRC) had failed to get to grips with the scale of fraud, carried out by non-EU sellers on such sites.
Its report said the traders' fast-growing and "illegal" practice of failing to charge customers VAT on goods housed in the UK was anti-competitive as it allowed them to undercut rivals by at least the 20% tax rate - putting UK retail staff out of their jobs.
It said the online platforms hosting the sellers were making more money than they should as they were raking-in commissions on sales that should have been blocked.
The committee described HMRC's estimate of an annual loss to the public purse of up to £1.5bn as "out of date and flawed" and hit out at its failure to bring any prosecutions under new enforcement powers.
It urged officials to ensure, by March next year, that online platforms had imposed greater VAT controls on non-EU traders - with Brexit likely to exacerbate the problem as new trade arrangements become clearer.
PAC chair, Meg Hillier, said: "HMRC needs to be far tougher in protecting the interests of British businesses and taxpayers.