One of our recommended shirtmakers, TukTuk has branched out a bit into other clobber and accessories of late, but they're still doing reasonably-priced shirts, including some new short-sleeved shirts for spring and summer.
Not obviously mod, the shirts are well-fitting button-downs, with the option of going bespoke if you want to add in some detailing. The one pictured above is the Summer Breeze floral short with 'v' and hem detail, a straight fit, button down collar (including back) and box pleat, made of 100 per cent cotton. That sells for £55.
See over the page for the Chaplin check shirt too. That's got a 2-inch collar, slim cut and locker loop on the reverse. £55 also for that. Check out the website for all the new items, including some big check ginghams.