A simple explanation of why the Axis Powers lost the war is that by 1942 they were facing a Grand Alliance that massively outmatched them in raw materials, manpower and productive capacity.[1] Which between them outproduced the Axis in all types of war material - tanks, artillery pieces, infantry weapons, combat aircraft, warships etc. However, within that framework Britain (plus its Commonwealth and Empire) is sometimes seen as "the weakest link", unable to survive on its own post Fall of France due to its economic inferiority to Nazi Germany with access to European resources.[2] (This may have been discussed earlier, so please guide me to any such long-gone thread!)
(1) Is this perception of Britain true? And how can we decide which of the two powers could produce the most war material in circumstances different from OTL?
FWIW Harrington (Table 1.6, pp. 15-16) shows the UK (which I hope includes production in the Dominions and Colonies) as outstripping Germany in combat aircraft, machine pistols (a surprise?) guns and mortars, and major naval vessels [3]. Germany outproduced the UK in rifles, machine guns and tanks/SPGs. Adding Italy to the European Axis total would give them a slight superiority in combat aircraft too but nothing else
(2) Can we conclude from this that that the UK (and Empire?) by itself was a match for Germany and Italy in production terms?
Indeed, depending on how we weight the separate categories of armaments and differentiate further [4] we might conclude the UK etc. did indeed outproduce Germany and even Germany and Italy. (Is it worth me doing such an 'Index of War Production'? [5] ) It would probably need just a bit more granular data than Harrington's, some of which I can probably find. The techniques for aggregating output of different classes of goods are fairly standard and i can (re)learn them, with a PC it's much easier than it was 30-40 years ago!)
(3) IF confirmed, how does this affect how we view the UK's strategic position in July 1940?
The decision to fight on after the Fall of France (and before Lend-Lease) may have looked insane to outsiders or even with hindsight. However, according to Edgerton it was taken by a British establishment still confident about its economic potential. Possibly slightly too confident but this emanated I think not from its view of British war production versus Germany's (accurate enough). Instead it overrated Britain's forces ability to turn technology into war-winning operations and tactics. For instance, the UK over estimated ASDIC's effectiveness so losses to U-Boats were higher than anticipated. See also the ineffectual perfomance of Bomber Command in 1941-2 as against expectations of what damage it could do to Germany.
Sorry this is so long but it's basically three questions and background information. Happy to reformat it if requested.
[1] Harrington, Table 1.2, pp. 7-8 suggests the differential in GDP wasn't massive (1.3:1) but this was using 1938 figures for Axis conquests like France. Which were not perfectly integrated into the German productive system and in any event had suffered sharp declines in GDP since 1940.
[2] See my recent friendly discussions with Wiking on a few threads

[3] Harrington's definition includes submarines but excludes torpedo boats, landing craft and auxiliaries. I'm not sure whether the many small sloops and other escorts produced in the UK are included.
[4] Example: For combat aircraft should 1x4-engined plane = 2x2-engined planes and 4x single-engined planes? In terms of war fighting capability maybe not this exactly but in terms of production capability some degree of weighting like that is needed.
[5] Ideally, has some post-grad done it already?
Sources available to me ATM, plus OU material and other books on the war.
Edgerton (2012),
Britain's War Machine, Penguin
Ellis, (1990)
Brute Force, Penguin hardback
Harrington (1998)
The Economics of World War II, Cambridge U iversity Press
Tooze, (2007)
The Wages of Destruction, Penguin