Well, the Cold War will certainly be...interesting, for lack of a better term, depending on whether or not Britain not surrendering somehow leads to a Nazi defeat or just some kind of stalemate and white peace (unlikely but not impossible, but I've seen plenty of scenarios based on this). If it's the former, you might get something like Robert Harris's Motherland novel, where instead of a cold war between the US and Germany, you have a cold war between the US and Soviets, and Europe is divided between east and west for lack of a better term. Of course the main events of that novel, if I remember correctly, where there's a crisis over Cuba over nukes (which in the novel are mentioned as having been developed during the Second World War by the US in 1945 instead of during the Third World War in 1985 like in our world) probably aren't going to happen. Don't get me wrong, it's a great novel, with tons of cool stuff like President JPK Jr's younger brother Jack Kennedy being the President instead of him, but lets be honest, the novel making Castro into a Communist instead of a diehard Fascist was frankly ridiculous.
Anyways, if it's the unlikely second option, where there's some kind of stalemate or white peace, where Germany still rules over Europe but Britain is independent, then you could see some huge differences in the Third World War, which I assume still happens. If the Allies had a foothold to get into Europe, it probably would have been much helpful, and maybe we could have avoided the need for looking elsewhere as a landing area, which could butterfly away the disastrous Allied defeat at the Battle of Gibraltar, which may not have even happened.