I'm surprised that you can't find one at Charles Tyrwhitt, as they've got quite a wide selection.
CT shirts aren't fantastic, but they're perfectly serviceable and better than pretty much all of the business shirts sold in DJs and Myers.
They offer pretty much all of their shirts with an option of either a French cuff or a single, button cuff.
Here are a few options from the CT website, all of which are available with a single, button cuff:
The above are all slim-fit. I know that CT also offer a smaller variety of shirts in an even more fitted cut, and they also have a rather baggy, "classic" cut.