At first glance that looked like the UK Royal Coat of Arms but, when I zoomed in, it appears to be a non-standard variation of that. The first quarter of the shield has the three English passant guardant lions (or at least an approximation of them) and the third quarter has what looks like the harp of Ireland. The second and fourth quarters are a bit of a mystery though. The second quarter looks nothing like the usual lion rampant for Scotland and I don't recognise the fourth quarter at all (usually that would be the English lions replicated). The armorial achievement at the bottom does appear to be "Dieu et Mon Droit", as is usual. There also appears to be some kind of beadwork running down the back of the unicorn on the right, which I've never seen before.
My guess is that this is some kind of fantasy design, subtly altered to suit some unofficial commercial purpose or perhaps to avoid censure for unofficial use of the arms. It's a bit small for a blazer button, unless from the sleeve. Waistcoat is also a possibility.
If the maker was following protocol (maybe we can't be too sure about that) then the armorial has the "Tudor" crown, in use between 1902 and 1952/3
Perhaps more will be revealed after you've cleaned it up.