The UK in many respects came out of WWII in a weaker position. It's cities where blitzed Rationing didn't end until the 50's for some products It took circa 50 years or so to repair it's war debt to the US under the lend-lease programme It started the war in essence as a Super-Power and at best ended the war as a Major-Power. But back to the topic question, one thing that might have come out of the war was that most of the Major power had lost many of their older ships the ones being more obsolete and came out with fleets of newer types of vessels. With now doubt several other new designs coming off the production lines.
This broadbrush ignores numerous significant realities, most importantly that the British economy was already foundering in the 1920s and 1930s. Most of that was due to a 15% contraction in exports and the difficulty of turning the economy around from what were becoming less profitable sectors, most notable steel and cotton cloth. It was almost impossible to maintain the two-power standard without the contraction of competing navies (because of global economic crises of the 20s and 30s), and by 1936 it was abandoned. And while some rationing continued, in part because the global economy was still struggling to meet demands in the early 1950s, the British economy was "recovering" quite well, so much that British politicians of the 50s and 60s referred to it as a "Golden Age."
Don't think anyone said you were. Just that that position is based more on wishful thinking and speculation than anything canon. The Federation is "us", after all, and who doesn't want to imagine themselves as number one? The closest we have to canon puts the Federation and Romulans as more or less evenly matched. At least until the supernova.
Winners Prophets: Positioned to regulate interaction between Alpha and Gamma Quadrants, thus contact between Federation and Dominion. Proved ability to intervene in military affairs. Federation: Increased ability to build ships of the line. Political prestige of organizing major assault on Cardassian territory, especially Cardassia itself. Survived attacks on core worlds. Functionally allied to the Prophets, who control conduit to Gamma Quadrant. Position symbollically recognized by other powers as negotiations and treaty signing held at Bajoran-Federation station Deep Space Nine. Klingon Empire: Intimate ally of Federation. Recognized for sacrificing men and material in key battles. Removed erratic leadership. Uncertain how new chancellor might reform empire politically and socially. Bajor: Minimal impact of "occupation." Pivot of Federation's relationship with Prophets. Political assistance to Federation and allies. Bajoran now commands Bajoran-Federation Deep Space Nine at junction to Gamma Quadrant. Romulan Empire: Difference in overall course of the war. Developed working relationships with Federation and Klingon Empire. War caused internal political and social unrest, whose resolution after the fall of Shinzon is unclear. Losers Cardassian Empire: Complete fall of government and occupation. Major loss of civilian life. Major loss of production capacity. Depletion of leadership class. Unclear direction with decapitation of liberation movement at end of war. Breen: Sacrifice of men and material in war effort. Not clear if any part of war was fought in Breen territory. Neutralization of weapons advantages. Embarrassment of defeat. Founders: Politically and militarily ejected from the Alpha Quadrant. Loss of Cardassia and Breen as Alpha Quadrant allies. Potential for political reforms with return of Federation changeling. Unclear what effect loss would have on control of worlds in Gamma Quadrant. Unclear what effect the integration of "Alphas" into general Jem'hadar might have. Loss of leading diplomat. Arrest and imprisonment of leading Founder.
I jsut find it hard to believe the Romulans were really that powerful. In Trek, the D'deridex class Romulan warship was pretty much the only ship we ever saw from the Romulans. And that ship was on par with the Galaxy class, which might as well have been a cruise ship. If the Federation actually decided to build warships like the Defiant and Akira, it would seem like the Romulans, who built the D'Deridex as a true warship, would all behind. ...And yes, I am completely biased towards the Federation.