Once a tariff is set, it's set for every country who wants to sell you those goods. In any trade deals we try to do we will be wearing those shackles

We already wear those shackles when trading outside EU, but EU sets them not us.
Soon we can set zero tariffs on foods we can not grow ourselves.

As we import far more goods than we export, we will be at the mercy of other countries who don't like what we're doing, consequently setting their import tariffs high.

No. As you said they have to have the same tariffs for all.

China makes stuff but we don't. You whack high tariffs on China and they'll stuff us.

No. They have to offer us the same tariff as EU and everyone else. No increase when we leave.

Keeping the tariffs low will flood the country with cheap goods and we'll end up making even less stuff.

No. We can choose which goods to tax.

And all the time we will be in a tariff environment with the EU, making our goods even less competitive than they are now.

Yes, and theirs even less competitive too.