Your button shows two Old-English Script letters below a British royal crown, so t is definitely one of the varieties of British Army "Named Regiment" buttons. I'm not sure about the identify of the letters... perhaps they are an I and a T. I was only able to eliminate some letters. I searched for a matchup at a webpage showing British Army named-regiment buttons but had no luck.
Militarynamedregs
Perhaps you'll have better luck by doing a search of the British Army buttons at the United Kingdom Detector Finds Database (UKDFD).
If your gilted (goldplated) brass button is a 2-piece button, it can date anytime from the 1830s to the present. I think yours is from the latter-1800s to early-1900s.