Two of the better known tailors in Bangkok are the Rajawongse Clothier and the Raja Tailor, both on Sukhumvit. Rajawongse dressed every US president from Reagan to Obama and the business cards on the wall of their changing room reads like an international who's who. They also dress most of the US Secret Service agents based in Bangkok. Their house cut is more to the American taste than to the British one. So, if you prefer your suits more fitted and double-vented, be sure to state that from the outset.They are practically right outside the Landmark Hotel. Incidentally, the chaps who own the Rajawongse Clothier also own the Radisson Blue hotel in Sukhumvit. That tells you how popular their tailor's shop is.
The rival Raja Tailor, on the other hand, is run by the brother of the guy who owns Rajawongse and they have their own list of celebrity clients. You get a more personalised service at Raja. The owner's daughter is a pain in the neck , but his son is a pleasure to deal with. The real Raja Tailor is located on that bit of Sukhumvit Road almost directly across from Soi 11, where the Ambassador Hotel is located. If you are standing at the mouth of Soi 11, the Raja Tailor will be on the opposite side of Sukhumvit Road, diagonal at about 2 o'clock. You probably won't see it immediately though, because it is now hidden behind the pedestrian overhead bridge. Take note though, that if you are standing at the mouth of Soi 11, immediately to the left will be another tailor shop with a huge red signboard saying "The World Famous Raja Tailor" or something like that. That is a completely fake one trading on the name of the original one, which is now hidden behind the overhead bridge.
Both these shops started-out during the Vietnam War era and are well-established. I used to use the Rajawongse, which still has a slightly better selection of fabrics, but I switched to Raja because it has better service.