Britons now know how Americans feel. The most politically polarizing U.S. President in modern history decided on Friday to inject himself into the British debate over the June referendum to leave the European Union, as ever leading with a dubious political threat.

President Obama spoke at a joint press conference with Prime Minister David Cameron, who is leading the Stay in the EU campaign. Mr. Obama began, as he often does, by saying that he wasn’t going to do what he then proceeded to do.

In this case he announced that he wasn’t trying to influence any British votes, and he wasn’t issuing a “threat.” But he went on to attack the argument of the Leave campaigners who say that, if the Leave vote prevails, the U.K. could strike trade deals that have similar benefits without the EU’s bureaucratic barnacles.

“And on that matter,” Mr. Obama said to British voters, “I think it’s fair to say that maybe some point down the line, there might be a U.K.-U.S. trade agreement, but it’s not going to happen anytime soon, because our focus is in negotiating with a big bloc, the European Union, to get a trade agreement done, and the U.K. is going to be in the back of the queue—not because we don’t have a special relationship, but because, given the heavy lift on any trade agreement, us having access to a big market with a lot of countries—rather than trying to do piecemeal trade agreements is hugely inefficient.”