I used to make quite a few windsor chairs in the 80's when the market was flooded with Elm that had been felled due to Dutch Elm Disease. I kept a few thick, wide Elm seat blanks, enough for half a dozen more single board windsor seats, but so far I've never gotten around to them. Elm is still available, mainly from some Scottish timber yards. It tends to be Wych Elm rather than English Elm, but from a practical user's perspective the difference isn't all that great. However, the majority of the Elm that I'm seeing now is planked to a maximum thickness of 50mm, where as for a really deeply saddled windsor you're better off starting with a 55mm or 60mm billet.
If your plan is to paint the seat then Tulip Wood (Poplar) is a good choice, or if not Alder, but you might get lucky and find thick boards of Tulip Wood that are a creamy white without the signature green streaks. At a pinch you could use Sycamore, but that's getting a bit hard for deep saddling with hand tools. Ash and Oak are harder still. It really is one of those timber selection jobs where you want to get down in person to the yard and pick your own boards.
Good luck!
