At all 3 unis I've attended, you wouldn't get marked down for convoluted logic (as long as it's right); Oxford would seem a bit unusual in this respect. (And I'd be interested to know just how "style" is assessed - it's obviously rather subjective).
One thing I did hear back from an examiner was that when you set things out 'properly', you're more likely to get the benefit of the doubt if you do something a little dodgy (as much as anything because the examiner is more likely to fall into "autopilot mode" thinking "yeah, OK, yeah, OK, full marks").
I'd also say, (and a fairly high profile mathematician said the same thing, although I can't remember who right now - might have been Korner) that the approach where you "hide all the failed approaches, ugly calculations, and just present the finished proof as if "take
N=e1/ϵ2+913" was the most obvious thing in the world" isn't actually a very helpful way of presenting many of these topics.
A particular example I remember: there would usually be a question where you had to decide whether a certain set was countable. And these questions can usually be trivialised by making aggressive use of the fundamental theorem of arithmetic. [e.g. the set S of all finite subsets of N is countable. Proof: let p_n be an enumeration of the primes; given a finite subset A={a_1, ..., a_m} define
f(A)=∏piai, then f is an injection into N, thus S is countable].
It's neat, and very efficient in an exam, but if that's the only technique you know you're missing a lot of material. (I should perhaps confess it was pretty much the only technique I knew - but then I didn't actually go to the lectures for that course).
Edit: Have you read Littlewood's Mathematician's Miscellany? If you're a stickler for rigour, it's somewhat interesting to see his thoughts about it. [Roughly - not as important as ideas - any decent mathematician can put in the rigour after if needed. I was a little surprised].