No one can be sure what will happen if/when we leave the EU. With regards to imports into the UK, the plan is to have a temporary tariff, under which up to 87% of imports by value would be duty free. That would mean that most of the stuff coming here from the EU would be free of duties etc.

However...

Due to changes caused by our leaving there are likely to be some teething problems (to put it mildly) to setting up/agreeing new procedures for documentation etc required to import UK goods into the EU. This could well cause delays to vehicles entering the EU from the UK, which in turn will mean a delay to them reloading more of the EU goods that we need here in the UK.

With any change in procedures there are likely to be some problems. They will be overcome. With regards to panic buying here in the UK, that too should settle down after a short while.