I thoroughly enjoy speculation like this and find it all too rare in most AH. Some things just would be different.
In my ATL 'Bentham' (premised on curtailing the Romantic Movement in Europe), fashions in the 1950s world are basically Victorian Lite. 'Reform' dresses for women are popular, though many still wear the full rig and corset for occasions, and men wear cutaways for formal attire, three-piece suits for the office, and lighter-coloured suits (often without the waistcoat) for leisure. Youth fashion is based on the 'practical man' (a cultural fad of the times), with denim or corduroy trousers, flannel shirts, leather caps and jackets, and boots for men being the height of 'rebelliousness'. It is chic for academics to know how to do plumbing or repair electrical wiring. Girls wear daringly short, tight skirts (up to almost the knee) and blouses either stiffly ironed, or loose and fluffy. Women's coats and jackets are mostly traditional. The previous fashion colourful 'primitive' African and India fabrics is almost completely over, the only multicolour varieties permitted today being checkered or plaid shirts for men. Everything else is solid monochrome or, at best, slightly variegated.
'Practical' women smoke - the whole 'practical' fad has done wonders for women's liberation throughout. The primitivist fashion had sressed them up in impractical swathes of beautiful cloth, as objects of art and admiration. The modern woman wears work clothes because she does useful work. Even wifes of wealthy men take part-time jobs - it's the done thing. Men have been smoking for generations, though cigars, cheeroots and hookahs are going out of fashion quickly in favour of new ceramic-lined Bakelite pipes and cigarettes. Even pipe smokers prefer unaromatised tobacco blends. Urban sophisticates have taken to the 'Bob-and-Six', the Marihuana cigarette imported from Africa and India.
Europe is subject to fashion influences particularly from two areas: Canada, the industrial giant of the Americas, exporting its 'Tonk' music and the attendant clothing style (flannel shirts, tight denim trousers, drover boots, broad-brimmed hats and lined jackets with plenty of pockets. The broad, tooled leather belt is indispensible with this gear, and if you can play snares and electric banjo you'll have the copines all over you). 'Tonk' slang includes many Quebecois loan words. The other, slightly more 'respectable', cultural influence is the Indian Rim, the rising economic power of the day. Gentlemen in London's muggy summers are often seen sporting collarless, straight-edged 'Delhi shirts' of thin silk-cotton blend (the more daring ones wearing them outside the beltline) and single-breasted open linen jackets. Trousers legs show decidedly less taper, and the ironing crease is no longer de rigeur. Women occasionally go even farther in this fashion, opting for tight tops (though not navel-free) and sarong-style skirts with linen jackets. Strangely enough, the traditional sari would still be regarded every bit as scandalous on a white woman in London as the new 'Indian' fashion would be in India.
Enough said. I'd really like to hear what others have come up with in their worlds