Over her we do use 'in shirtsleeves'. A phrase that is definitely on the wane is 'shirtsleeve order' - used chiefly by people with a military background (and by people who went to fee-paying schools that had a "Corps" - boys playing at being soldiers, but with real - if old - equipment).
When it was hot a soldier could not remove his uniform jacket unless his superior had announced 'shirtsleeve order'. The Test Match Special (BBC, cricket) commentators have the appropriate background, and they frequently say things like 'It was shirtsleeve order at Lords today'.
I love to listen to the American football commentators, esp. the "color guys," try to find something clever and informative to say. Best Ever: "The quarterback's down in the end zone nursing a hurt calf."
And I should probably have explained 'Lord's' - so-called 'home of cricket' - not as big as 'The Oval' (London's other cricket ground), but more central, in a more fashionable neighbourhood, and generally more venerable (among cricket-lovers).