Thicker walked ceramic mugs are definitely common in the UK, and probably more common now than anything else, but me and my gran both agree that a proper cup of tea needs serving in a thin-walled, fine-china cup, like this: https://fegghayespottery.co.uk/product/plain-270ml-bone-chin...
In the States indeed these mostly look like bog standard coffee mugs. The tall one exists as a design but it’s rarer. I can’t speak for the OP but my experience is that media about Great Britain in America often depicts tea mugs as different (I’ve seen many shorter, smaller and flatter variants) than those mugs. Perhaps it is to highlight that the beverage is tea and not something else like coffee to the viewer.
> one should drink out of a good breakfast cup—that is, the cylindrical type of cup, not the flat, shallow type. The breakfast cup holds more, and with the other kind one’s tea is always half cold—before one has well started on it.
So I suspect that "tall" is a byword for "not shallow".
This is probably the most common shape you'd expect to see in someone's house: https://i.etsystatic.com/7320577/r/il/c46fa1/1742208467/il_f...
A more stylish approach would be like this: https://teaunboxed.b-cdn.net/wp-content/uploads/2020/06/tea-...
This is what you'd probably get in a standard cafe: https://1975.me.uk/wp-content/uploads/2014/05/Great-British-...
This is what I think of when someone says "tall" mug: https://uk.pinterest.com/pin/269441990179867455/