Once again complete supposition. Why would the EU put huge trade tariffs on us? They like trading with us and would want to see it continue.
Another case of a remainer not wishing to state just how great the EU is, as it's not, but simply trying to scare people from voting for freedom.
Sent straight from the boot of Lingard
The EU will be happy to provide tariff-free access if we allow free movement of people. That's clear. However, the majority of Brexit voters would appear to be voting Leave because they want to be able to impose restrictions on the free movement of people. Hence, if we leave, the EU would impose tariffs. It's very simple. A Brexit vote would be politically calamitous for the rest of the EU, and they would HAVE to make sure no other country followed suit. It is absolutely in their interests to make things as uncomfortable as possible for us, post-Brexit. I'm sure if we were in their position we'd do the same.
I don't think the EU is great - far from it. It's just the lesser of two evils. Better the devil you know....