Yes trading will continue of course, the purchase and sale of goods will continue. Just in a different and more inefficient way.
Tariffs are one concern but is not the major concern.
My main concern for the UK is the frictionless border - it is vital that goods are able to move freely back and forth because they will between the other 27 EU countries.
If the current frictionless border develops friction, ie if the UK leaves the CU/SM, then companies eg Airbus, BMW, Nissan etc will move their production to the area where there is no friction, it is not to punish the UK like Hunt seems to think, it is vital in the production.
Trade does not operate like in the 1960s like some people think. It doesn't even function as in the 1980s or even 1990s.
And goods are only one part of the problem.