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I’m in east London with an almost identical sized bathroom that was refitted 5 years ago. Even though prices will have gone up significantly, £18k sounds absurdly high. Mine was 1/3 of that – £2.5k for materials/fixtures (mid range quality, self-sourced) £5600 labour. Included moving toilet and plumbing. I recall quotes varied wildly – his wasn’t the cheapest, and local high-end bathroom specialist shops were up at £15kish dep on fittings.
I also wouldn’t bother rehanging the door given it’s in its own nook – besides opening inwards affords privacy if someone happens to already be in the bathroom (my bathroom door is identical to yours in that little nook!)