LONDON — When Alfred Smith and Bob Weighton were born, Edward VII was king of Britain. They have lived through two world wars, more than 20 prime ministers and the entire rule of Britain’s longest-reigning monarch. They also saw Britain join the predecessor of the European Union — a bloc it was supposed to leave on Friday, the day both men turned 111.

As it became clear that the withdrawal known as Brexit wouldn’t happen on his birthday after all, Mr. Weighton, who lives in southern England, echoed a growing frustration with the current political deadlock, calling it “a total mess.”

“My own feeling is that if there were defects — and there were quite obviously defects — we can negotiate on the inside rather than walking off the field with the cricket ball and saying ‘I’m not playing,’” Mr. Weighton told the BBC.

But the most common question he has been asked does not concern politics. He said most people wanted to know the secret to his longevity — something to which he could not respond.