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A friend of mine who is 6'7" used to go to High & Mighty and always pronounced himself happy with what he got there.
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Charles Tyrwhitt have a few stores in London. I buy their extra slim fit shirts, which are more of a regular fit on me (their regular fit is aimed firmly at the middle aged spread crowd). The big benefit for me is they do three different arm lengths for each cut and neck size, so you can "tailor" it a bit. I buy everything online, but I'd try a few in store first.
The advantage of these pseudo-tailor type stores (Tyrwitt, TM Lewin and the like) is that they tend to keep the same cut as standard for several years, so once you've got a good fit you can just buy online and get a consistent result.
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I had this problem recently, needed a shirt in a pinch. Ended up at TM Lewin's Jermyn St store where they stock 35" arm slim fit shirts. I'm 6'6" with a 15.5" neck and they sorted me out. Any longer in the arm and you need to order online.
Also would recommend TM Lewin as they let me bring my bike into the shop and wander around picking a shirt whilst in lycra.
I'm very tall and fairly slim with long arms, and I'm after some smart shirts for work that don't resemble tents in the larger sizes I need to buy for the length.
Are there any high street shops that cater for such proportions?