Here's my idea for how Britain could have won the war alone:
First things first, one change must occur before the outbreak of WW2 - Japan must not become overtly militaristic during the 1930s, and they must remain friendly towards the Western Allies. That way, the Second Sino-Japanese War never happens, and by extension WW2 never extends to the Pacific Theatre. Instead, during WW2, we have Japan supporting Britain (albeit remaining officially neutral) and remaining with its post-WW1 borders, while far less British troops need be stationed in the East.
Meanwhile, WW2 breaks out and proceeds initially as it did in our timeline. However, events start to change following the Battle of Britain - after the RAF is able to decisively defeat the Luftwaffe, Hitler decides to try and save face by by launching Operation Sealion anyhow (maybe in this timeline he is even more incompetent in military affairs than in our timeline).
And so, the German forces start to cross the Channel - unsurprisingly, they are overwhelmed by Royal Navy ships which bombard them from the sea, and RAF planes which bombard them from the sky. This cripples the invasion force to the extent that most of the invasion fleet is either destroyed or forced to turn back, and only a few landings take place in Kent. These German landings are quickly overwhelmed through a combination of British regulars and the Home Guard - after only a few days of fighting, the Germans are forced to surrender, and thus Britain has secured a major victory. Meanwhile, the botched landings have crippled the German Army significantly - the Luftwaffe and the Kriegsmarine are all but annihilated, while a lot of supplies and equipment have been lost.
With the threat of a German invasion almost entirely gone, during 1941, Churchill and the British Government are able to dedicate more troops to the front-line who IOTL remained stationed in Britain. This means that Operation Compass results in further advances by British and Commonwealth forces in Libya (eventually leading to the entirety of Libya falling under Allied control by the end of 1941), while British and Greek troops are able to hold Crete (as German paratroopers were crippled in the botched Sealion landings). Meanwhile, Iraq and Syria, and Italian East Africa are still secured by British and Commonwealth troops at the same time as OTL.
During this time, the US continues to send support to Britain through Lend-Lease and other agreements, although the US has no appetite for actually entering the war (no conflict in the East, no Pearl Harbour). In addition to this, Britain is also dedicating a significant amount of funding towards Tube Alloys (the development of an atomic bomb).
As 1942 dawns, Britain and the Commonwealth are in a strong position, and aim to knock out the final Axis outposts outside of Europe. Operation Torch is launched several months earlier than IOTL, and has the same outcome - French West Africa is liberated by British, Commonwealth and Free French troops, and shortly afterwards Tunisia is also liberated. As a result, all of Africa (aside from Portugal's colonies) is under the control of the Allies by the end of 1942.
Now, at this point I shall accept your 'bonus challenge' - in this timeline, Barbarossa is delayed, due to the damage inflicted on German forces as a result of the failed Sealion landings. So, it is launched in 1942 rather than 41 (Axis campaigns in the Balkans still occur in 1941, though). Let us assume that, during this alternate invasion of the Soviet Union, events go better for the Germans, and thus by mid-1943, German troops have reached Moscow. Shortly afterwards, the Soviets are forced to sue for peace, and Germany annexes all of Russia up to the Urals, and beyond there a rump Soviet state exists.
Yet the Allies do not despair at the Soviets' defeat, for, during 1943, plans are drawn up by British, Commonwealth and Free French troops for landings in Sicily as preparation for an invasion of mainland Italy. At this point, Italy is incredibly unstable, as the loss of its colonies means that there is a major oil shortage in Italy, and many Italians blame Mussolini for their country's setbacks during the war. In mid-1943, landings take place in Sicily, and (like IOTL), the island is overrun after several weeks. From this point, the Italian Campaign plays out along similar lines to OTL (although Allied advances are slower, due to a lack of American troops) - Mussolini is overthrown, Italy requests an armistice with the Allies, Germany invades Italy and installs a puppet regime, and so the Allies start a full-scale invasion of Italy. Eventually, in this timeline, the Italian Campaign comes to a standstill in mid-1944 as fighting comes to a standstill near Rome.
In this timeline, the D-Day landings do not take place, as not enough troops are available to undertake such an operation. However, during this time, Tube Alloys is proceeding well for British and Commonwealth scientists, and by early 1945 Britain has tested its first atomic bomb in the Pacific Ocean. In order to force Germany to surrender and bring the war to an end, Britain drops an atomic bomb on Hamburg. Shortly after dropping the bomb, Britain demands that Germany surrender, or face further attacks. Hitler refuses to surrender, and so another atomic bomb is dropped on Bremen. At this point, may German officers are terrified that Germany could face annihilation due to Hitler's stubbornness, and so an Operation Valkyrie-style event occurs which sees the military successfully depose the Fuhrer. Shortly afterwards, a military junta assumes control in Berlin, and requests an armistice from Britain, bringing an end to the Second World War.
As part of the Treaties ending the war, borders in most of Europe are re-set to their state before Hitler's rise to power - the exception is the border between Germany and Poland, with Poland gaining the territory it gained from Germany ITOL, all the while retaining its territory in the East. In addition to this, Italy's colonies are partitioned between Britain and France, while Heligoland is ceded to Britain. Meanwhile, Russia ends up in a similar state to what it was in the Anglo/American-Nazi War Timeline, with the Soviets still controlling Siberia and European Russia being established as either a Russian Republic or a restored Russian Empire.
In this alternate post-war world, Britain and France are still dominant in Europe - Germany has been humbled and demilitarised, and the nations of Europe are on friendly terms with the Allies. Meanwhile, on the global scale, Britain continues to dominate world affairs for several decades longer, while the US remains isolationist unless something major happens during the late 20th century.