OLAF recently concluded an investigation that revealed a "major pattern of customs fraud" caused by the declaration at customs of "falsely low" values for textiles and footwear imported from China, it said.
"This is an example of so-called undervaluation fraud, whereby the goods are declared at a fictitiously low value at import so that importers can derive profit from evading customs duties and related taxes, paying much less than what is legally due. The most significant hub for this fraudulent traffic was found to be in place in the United Kingdom," OLAF said.
Between 2013 and 2016, criminals evaded customs duties using fictitious and false invoices and incorrect customs value declarations when importing through the UK, it said.
"These fraudsters are in fact organised crime groups whose actions affect the entire EU," it said.
The imports arrive for custom clearance in the UK, but are destined for black market traffic in other member states.
The calculated €2bn in lost duties is ongoing, "since this fraud has not been stopped to date", it said.
The investigation also revealed VAT evasion worth around €3.2bn on imports through the UK that are destined for other member states, OLAF said. The evasion uses a customs procedure relating to the suspension of payment of VAT for goods in transit towards other member states.
OLAF has sent a recommendation to the European Commission's directorate-general for budget, saying that the UK should repay the €2bn to the EU budget, and to the directorate-general for taxation on the abuse of the customs procedure.
The office has also sent an "administrative recommendation" to HMRC on how to reduce the risk of undervaluation of taxes on imports of textiles and footwear from China, and how to recover "to the extent possible" the duties that have been evaded.
It has also recommended that the UK Crown Prosecution Service initiate proceedings against those involved.