You are using an out of date browser. It may not display this or other websites correctly. You should upgrade or use an alternative browser.
alternatehistory.com
So in 1862 there was a greek referendum for a new king - Prince Alfred of Great Britain got 95% percent of the vote but still wasn't chosen, partly because of the London Conference of 1832 setting a precedent that Great Powers wanted to follow, but also because Queen Victoria was strongly opposed to sending a son off to a foreign country. So let's say she isn't quite so opposed (Prince Albert lives or something) and Alfred becomes King of Greece in 1862.
Now let's have a second POD of the Prince of Wales dying in 1863 (before conceiving Albert Victor, let's say), putting Alfred directly in line to the British throne. What exactly happens now? A personal union of the two countries really isn't going to fly - but all the alternatives are also awkward. Does Alfred abdicate the Greek throne after reigning for a year? Does he give up his claim to the British throne for his brother Arthur, Duke of Connaught? (Does Arthur somehow become King of Greece?)