If trade barriers are removed then countries can take full advantage of comparative advantage. Countries specialise, trade more and as a result not only do the costs of goods fall, but everyone is better off.
As the EEC became the EC, then the EU the process of greater integration has continued and the pattern of UK trade has changed.
In 1973 the USA was Britain's largest trading partner. At some point in the recent past France overtook the USA as our biggest trading partner (I missed that too) and now it is Germany. France will be crestfallen, but who cares?
Recently a government economic adviser claimed that the benefits of joining the EEC were pretty weak and only based on trade. According to him the benefits have been as weak as expected.
