This is not true as there is ‘free trade’ only within the EU. As far as the rest of the world is concerned, the EU is a customs union which imposes tariffs on goods from outside it, in particular agricultural products. This means higher food prices; which was one reason why some were opposed to British capitalism joining the EEC (as the EU was then called, more accurately) in the first place in 1973.
This is still the case, as Gerard Lyons, of Economists for Brexit, pointed out in an article in the Times (6 May):
So, if British capitalism left (and if it is decided not to protect UK farmers – a big If) there would be lower food prices. But this would not benefit workers. Lower food prices by reducing the cost of living would lead to lower wages, leaving workers in the same position as before. So, while this might earn them a point against the Remain camp, it cuts no ice from the working class point of view.