This argument is often given by the Vote Leave campaigners, without any evidence to back this up. It is an argument based on pure arrogance of British superiority.
However, negotiating strength in free trade talks is basically a numbers game. How big is your economy? This is a basic fact of economics.
By negotiating free trade deals as part of a body of 28 developed countries with a population of more than 500 million people, the UK has a much stronger negotiating hand than negotiating on its own with only a population of 65 million.
It's as simple as that.
As the UK is one of the strongest 3 members of the EU, it has been able to tailor the EU's free trade deals to include the services sector which is so vital to the UK's service-led economy. (And veto them altogether if they didn't meet the requirements!)
Including services in free trade deals is notoriously difficult and would be almost impossible to negotiate by the UK on its own.
Switzerland has often been cited as a country that makes its own trade deals without being a member of the EU. But Switzerland is a prime example of how difficult it is for small economies to negotiate trade deals with large economies. For example, Switzerland's trade deal with China (a much larger economy) gives China significant access to the Swiss market, but equivalent access for Switzerland to the Chinese market is withheld for 15 years!