Steve,
After brexit we will have to impose tariffs on those imports if we want to strike favourable deals with non-EU countries

That is bollocks Steve.
Where did you get such a ludicrous notion?
WE would choose which products required tariffs, and WTO says you can not discriminate between countries except by having free trade deals.
We only need apply them to protect UK producers.

EU would be self harming if they goad us into imposing tarifs against their exports. Their exports will already be less attractive to us without the tarifs against non-EU foods.

The imports already cost more because of the way the pound has soared downward,

That factor has caused a little inflation but has now moved through the system. It is no longer causing inflation.