The only nation (well, at least major - I'm not talking about the rash of countries that declared war in Germany in 1945 so they could say they were in the Allies, but didn't do anything) that I would describe as performing anywhere near and underwhelming fashion during WW2 would be Italy, and even then it had its moments, and many of its units were still top-notch. You've had plenty of evidence to highlight why it wasn't actually a poor showing, so I'll try and focus on the ones that haven't been mentioned, or elaborate on some of those that have.
The most important thing to keep in mind (after reading @FOARP's post covering WWI - in WWI the British had a first-rate army and a first-rate Navy, and pretty much bankrupted the Empire to do it - to describe their effort as underwhelming suggest's someone's research prior to posting has been a tad underwhelming as well) is that the British Empire paid very heavily for its success in WWI. Be it for out-producing Germany in Dreadnoughts, or fielding an army of the size it did, with the support it had, it cost them dearly, and they never recovered financially (or, by the start of WW2, emotionally and demographically).
So - as FOARP well puts it, they didn't underwhelmingly perform in WWI, anything but. I'd be interesting in knowing where you got this impression.
As for WW2, it's important to realise that Britain in 1939 was not Britain in 1914. The Empire may have been larger, but the combination of the drain (financial and demographic) of WWI, combined with changing economic and social practices (people in colonies wanting self-determination, which was a thing before WW2 and would have happened without WW2 - indeed, much of the British Empire didn't become independent until the 1960s, and while the subcontinent (which did become independent in the late 1940s) did become independent pretty much straight after the war, it had been agitating for independence since before WWI). Note, everything below uses 'Britain' for 'Britain and Commonwealth' for ease of writing - it's in no way suggesting Britain was anything other than one amongst a group of nations with a shared outlook.
Essentially, in the 1930s, the majority of the population (and Britain was a democracy, so this was a factor that the Government had to take into account) was strongly averse to war. Declaring war in 1938 would have been politically very dangerous, and a long war starting in 1938 with Britain looking the aggressor (and by 1938 it wasn't going to be a short war) could have destroyed whichever political party went down that path, and substantially increased the potential for a compromise peace and a far worse long-term outcome. The anti-war sentiment also limited how much money the Government could spend building up its forces and, given limited resources, the UK focussed on its navy and air force (although it still put significant effort into its army - of all the major combatants, Britain and the US were the only two that had first-class navies, air forces and armies).
So we've got British forces probably about as strong as they are likely to be, in the circumstances, at the start of the war. This means a Navy that's first-class, an airforce that's solid and growing quickly, and a small but very capable army, but one that was to take far too long to adjust to armoured warfare (and if you're looking for somewhere that the British were underwhelming, it was their bad habit of driving tanks into emplaced '88s in the western desert).
So what can we expect from this - we can expect that the British will control the seas (which they did in Europe, making some fairly bold moves in the Mediterranean that paid off, as well as a bold move in South East Asia that did not) and use the navy to ensure it can't be defeated, which it did. Had the British gone with a smaller navy and a larger army, it's far more likely that they would have been forced to surrender earlier. Further, a navy isn't a purely defensive endeavour, as the blockade of Germany in WWI proved (although trade with the Soviets pre-Barbarossa limited the impact of this until post-Barbarossa).
The air force put substantial pressure on Germany from the air (there were I think (and going from memory, so this could be a bit off) 2 million personnel manning Germany's air defences, and quite a few aircraft to - that's a pretty decent amount of manpower tied down by the RAF (initially by themselves and then in conjunction with the USAAF), and there was an impact on industrial production and morale (or those 2 million Germans would have been off on the Eastern Front, along with all their aircraft and artillery), although the extent of this impact is heavily debated.
From the army, we can expect that initially it can't do much more than be a 'pinch hitter', but will grow in time to make a significant contribution - which it did. The British and Canadians did the hard fighting that lead to the break-out from Normandy (and were expected to have the hardest beach landings as well, although the US got unlucky here and had by far the worst of it on the beaches), and a lot of the harder fighting on the way into Germany, until the Battle of the Bulge. Early on, the British Army helped slow the Germans during their charge through France and decimated the Italian forces in Libya, but were also strategically misused at times (the deployment to Greece was optimistic to say the least), but not to a degree less or worse than other nations.
Another thing to keep in mind - just like the British had to keep a significant portion of the RN in place to defend against the Kriegsmarine, the Germans kept significant forces in France to defend against possible Allied incursions, and after the invasion of Italy (of which Empire and Commowealth troops formed the majority of land forces), the Germans withdrew key units from the Russian Front to bolster the Italian defence, aiding the Russians at Kursk (I'm not suggesting they wouldn't have won at Kursk, but having fewer elite divisions to fight is always a good thing!)
Of course, I don't subscribe to the 'plucky Britain defeats monstrous Germany' myth either - Britain was a world power, with a naval focus, and should not have been in a position where it had to capitulate to Germany (and wasn't), but I'd say that it made a contribution appropriate to its capabilities during the war, and in many cases did well (while in others did badly). It's an incredibly (incredibly) difficult job to benchmark each of the powers' performance during the period, but it's far more complicated than saying "Britain was big, so why didn't it do more?" (particularly when it did rather a lot) - it'd be the equivalent of saying "Germany's GDP was bigger than Britain's, so why didn't it sink the RN and invade the UK? As noted earlier, the only nation which I think could have done significantly better (assuming they did the same thing, but better) would be Italy.
Hope that helps, just my 2 cents, but while the idea that Britain 'saved the world' by 'holding on against all odds' is obviously fanciful, suggesting they were impotent in WW2 (let alone WW1!) is equally off the planet.
Edit: I'm not trying to suggest the UK did it easily either - anything but - the Battle of the Atlantic is a good place to start looking as to why.
Edit 2: Removed the first sentence of my reply, which was unnecessary. Apologies, I wasn't trying to be rude, you just caught me early while my brain was still 'brittle'.
Bravo, good post and I agree with many points.