1) Germany + Italy. Navally and aerially, the British were already winning this one by Dec 1941.
2) Germany + Japan. Suez is open, several BBs not lost, more troops and planes for Malaysia... I think this one's debatable, but the British would be in with a fair shot since they could send almost the entire navy east and could hold Singapore, and their subs could ravage the Japanese merchant marine.
3) Italy + Japan. Simply replacing the warships the Germans sunk (Royal Oak, Courageous, Glorious, Ark Royal, Hood...) and the threat of the U-boats, would make things a lot easier for the Admiralty.
Granted, there's room for debate, but I think it's a reasonable position that the Brits would have had a good chance.
but look at their commitments ... the RN needs 2 KG V class ships and at least 1 carrier to watch the Tirpitz, Scharnhorst, Gneisnau plus at least enough heavy cruisers to counter the Scheer and Prinz Eugen (figure at least 2 apiece). Force H has to be maintained to block the approaches to Gibraltar and assist Malta and strong enough to at least equal the Italians, so 2 BB, 1 CV, plus escorts, preferably at least one or two more CV
The Med Fleet out of Alexandria needs to match the Italians so at least 2-3 BB, 1 CV or more if possible, and sufficient cruisers to match the rather sizeable Italian cruiser force
The R class ships are suitable only for escort duties, while the Nelson and Rodney are too slow for the Med or to face the Japanese (all of their ships are at least as fast as the Queen Elizabeth class).
That doesn't leave much available... if Pound is willing to risk it, he has 2 KGV class ships (King George V and the still working up Duke of York), plus 1 Illustrious class CV for Home Fleet plus several cruisers
2 Queen Elizabeth class plus 1 CV, 1 CVL for Force H plus cruisers
3 Queen Elizabeth class plus 1 CV plus cruisers for Alexandria
That leaves the Prince of Wales, both battlecruisers, the R class ships, and the 2 Nelsons plus whatever CV he can scrape up (the loss of the Ark Royal really hurts here, as does the hammering the Indomitable took at Crete)
so the maximum size of Force Z as a fast attack force is 1 BB, 2 BC, 1 CV, plus cruisers and destroyers, although possibly a second force with 6 BB (the slow R class and Nelsons) as a back up. There aren't many CV or CVL to be had, and the destroyers are already thinly stretched as the Battle of the Atlantic is approaching a very dangerous period.
The Imperial Japanese Navy looks at this force and may just decide that committing its 6 battleships is worth the risk to obtain Singapore and the Dutch East Indies and it may just get a decisive victory to force the British to the peace table early if they win (remember its what the Japanese may think, not what we think that matters here) OR Yamamato decides that instead of hitting Hawaii, the ideal solution is to keep the existing strategy versus the Americans (let them come, attrit them in the Marshal Islands and a decisive battle close to Japan) while the Carriers and Battle Fleet together move south to eliminate the British Navy