One difference that jars my attention is that British usage capitalizes some acronyms as a proper noun. American usage generally does not - we either treat it as an abbreviation or a regular noun.
I’ll see a British reference to Nato or Salt; an American would write it NATO or SALT. And if it becomes a common term like radar or scuba, we stop capitalizing it entirely.
There are other cases of differences which are truly grammatical, rather than the merely idiomatic in hospital.
British English tends not to use do-support for have as a principle verb meaning “possess”:
AmE – Virgin Atlantic has daily flights to New York, doesn’t it?
BrE – Virgin Atlantic has daily flights to New York, hasn’t it?
I don’t know prevalent or consistent this is in Britain, but my ear tells me that Americans seldom do this. But to get to the OP, whether Americans stopped doing this, or Brits started doing it–and when–is something I’d like to know.
Or maybe it’s a regional thing in Britain, and those regions took it along as they colonized, for the “British” way to fade out.
Here’s one from a meeting with an American colleague this week.
“We’ve discussed item A, and I think we should table item B.”
So we all waited for her to talk about item B, but she went on with item C. “What about item B?” we asked.
“We’re tabling it.”
In the resulting confused discussion we discovered that “to table” something in a meeting in the US (or at least the part where she’s from) means “to postpone” whereas here it means “to bring up”. The exact opposite.