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If you look more closely at the first button, in addition to the rose (for England) there is also a shamrock (for Ireland) to the left, and a thistle (for Scotland) to the right. I don’t think there’s much doubt it’s a British button.
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Britain legislated the minimum amount of gold required for a button to be called “Gilt”, “Double Gilt” or “Treble/Triple Gilt” in 1796 and terms such as “Rich Gilt” then began appearing as way of circumventing the legislation.
The backmark is indented, and those types of backmark began appearing around 1810 but, as a result of various embargos on trade followed by the War of 1812, almost no British buttons were exported to America between 1808 and 1816 (apart from a brief period in 1810). When trade resumed in 1816 most British manufacturers had removed backmarks that identified their buttons as British to avoid them being rejected by those with lingering anti-British sentiments. Some of them began using eagle backmarks to increase their acceptance in the American market.
It was a while before things ‘settled down’ so I think it unlikely that a button with such overt emblems for Britain would be prior to about 1820, and more likely post 1830-ish… assuming it was exported as such rather than a ‘personal import’ on a coat someone was wearing.
