Germany was already working on Projekt 47 (upgraded U-cruiser) and Projekt 50 (big turbine-driven sub that actually had its own smokestack) so without 15-20 years of design and development lag what do subs look like in the late 30s/early 40s?
This is pretty much the same as the other Naval powers. Despite some interwar experiment the British went to war with designs evolved from their late successful ww1 designs that entered service in the 20s and early 30s.Not much different. On a cost per ton basis submarines are an expensive capability, especially in peace time.
There was no real gap as the German Navy set up NV Ingenieurskantoor voor Scheepsbouw(IvS) in the Netherlands as an incubator for their submarine research and design knowledge. The technology had reached a plateau.
After the steam powered K class the RN wanted 20 2,200ton 22knot River Class Fleet Submarines but only built 3 due to cost and tonnage restrictions.The only major powers who had significantly different submarines by WW2 as compared to their WW1 subs were the US and Japan and that's mainly due to the planned fleet scouting/skirmishing role they had in the vastness of the Pacific
OP doesn't say what "CP win" means, but if England isn't invaded (which CP were hardly capable of), whatever peace the UK eventually accepts (presumably after the fall of France) will not involve the RN being dismantled. Lots of colonial territory being returned and maybe a little extra conceded, sure, but the UK would rather fight on indefinitely than give up RN, and the Central Powers did not want to fight on indefinitely.If the 'Central Powers' won, would France & UK even have navies beyond cute coast-guard cutters ??
Would surrender / armistice conditions have seen the RN scuttled en-masse at Scapa Flow, with the exception of eg Med & Far East ships that flee to Australia, along with Dutch, French etc ??