A significant burden is actually the lack of regulatory alignment. Before Brexit there was a largely customs-check free flow of goods in and out of the EU. Now we have more delays and paperwork. This is not a tariff, but it imposes costs like one.

That is true although it doesn't really change the point. The proponents for Brexit mostly wanted to free themselves from EU regulation and the voters wanted to cut down on immigration. The only people complaining about tariffs were remainers (including myself), we were arguing they would increase and we were wrong.