Having seen similar war of 1812 time frame buttons like the design of yours, i'd say the button dates sometime from the 1790s-1820s - perhaps the War Of 1812 time frame... I notice the back of the button is got a dome shape to it or maybe that is just the picture itself.. Does the area you are hunting in have any War Of 1812 activity? Adding the location of the button can help sometimes too.. The button in photo is a 1812 Royal Regiment of Artillery button with crown on it.
Edit: I just saw Iron Patch post about the correct ID. Typing @ the same time..
BTW you can thank Bramblefind for the ID. She wrote me and when I told you there was an ID likely coming in a minute, I just wanted time to compare to see how close it was. I actually had no idea on this and probably would have gone through every British regiment before getting to that. I do think I have laid my eyes on that type of button before, but it was many years ago... so I guess that tells you it's probably not the most common thing to dig in our parts.
Thanks Bramblefind and IP...I'll have another difficult one tonight...something else that's been taking space in my button box that is military but I have not been able to identify it...poor condition...