A "hard Brexit" will cost UK companies an extra £1.2 billion a year, it has been estimated.
The Open Europe group, which is campaigning for Britain to keep the closest possible ties with Brussels, said that would be the cost of UK withdrawal from the EU's free trade agreements with some 50 countries.
Labour former Cabinet minister Lord Mandelson said: "A hard Brexit could lead to a £1.2 billion bombshell for British businesses.
"The billion-pound bill for losing access to trade deals with over 50 countries would be footed by businesses and passed on to consumers with higher prices in the shops.
"Leave campaigners talk about all the free trade deals we can sign outside the EU but do not appreciate the value of those we already have. The EU is a leader in global free trade and we should seek to preserve its benefits, as far as is possible.
"The best way to keep these deals in place would be to negotiate for membership of the Single Market and the Customs Union. Doing so would be a big boost for British importers and exporters."