Its inquiry found that fraudsters evaded customs duties by using false invoices and incorrect customs value declarations between 2013 and 2016.
OLAF claimed that while several other EU member states took action to combat the fraud, HM Revenue & Customs (HMRC) continued to ignore the problem despite repeated warnings.
Its statement said: "These fraudsters are in fact organised crime groups whose actions affect the entire EU; they operate in criminal networks active across the EU.
"The OLAF investigation revealed that most of the imports arrive for custom clearance in the UK, but are in fact supplies destined for the black market traffic of textiles and footwear in other member states across the EU.
"Upon concluding the investigation, OLAF calculated a loss of almost €2bn to the EU budget in terms of lost customs duties due on textiles and shoes imported from China through the UK in the period 2013-2016.
"These losses to the EU budget are still on-going since this fraud has not been stopped to date."
Sky News was awaiting a statement from HMRC in response to the findings but a Government spokesman said: "We have only just received this report.
"We don't recognise the figures. They are currently being examined by HMRC.
"We have not received a bill from the European Commission. This report is not a bill, it is an estimate."
He added: "UK Customs takes all allegations of fraud seriously and investigates thoroughly.
"We would point you to their excellent record tackling fraud and rule-breaking, securing £26.6bn last year."
SKY News.