By Philip Blenkinsop BRUSSELS, Jan 21 (Reuters) - U.S. customs authorities will face a real challenge if President Donald Trump goes through with his threat to place tariffs on six EU countries - rather than the whole European Union - given the ease of movement of goods between EU members.

The 27-nation bloc struck a trade deal with Trump in July.

The US president has backed down in the row over Greenland after threatening Europe with tariffs and the potential use of military force

President Donald Trump signed executive orders on Saturday imposing his long-awaited tariffs on America's top trading partners. Mexico faces a 25% tariff, according to the White House, which said it will remain in place until the country "cooperates with the U.