Countries' control over imports is not absolute; they are bound by international treaties (at least in a game-theoretic sense). More specifically, everyone is a

Countries' control over imports is not absolute; they are bound by international treaties (at least in a game-theoretic sense). More specifically, everyone is a WTO member and the WTO sets rules on how countries are allowed to control imports. You are required to grant all WTO members the same level of market access, absent a comprehensive free-trade agreement. This is known as the "most favored nation" rule. So, the UK can't say they don't want to import German cheese. Once they allow any foreign cheese into their market, the MFN rule means they have to allow all foreign cheese into the market. Likewise, if they wanted to ban German cheese, they'd also have to ban cheeses from everywhere else. The only situation in which they'd be able to allow one country's cheese and not the other is if they had a comprehensive free-trade agreement or a customs union... you know, the exact sort of thing that they just left.