The first is an old style 4-hole button with maker's marks on the front and back. They were hard to read and took some guessing and Googling but I think I got it in the end.

image by g.nat, on Flickr
The rear name is Firmin and Sons, London which I've found are one of the oldest companies still in operation today (founded in the 1650's.)

image by g.nat, on Flickr
The name on the front is Austin & Oaker of 11 Conduit St. and they seem to have been tailors and outfitters producing mainly military stuff. Possibly around the 1870's - does that fit with the button design?
Then I found this.... A French Foreign Legion button!! (Still with thread attatched!)

image by g.nat, on Flickr
At first I was pretty excited, wondering how it came to be on a beach in the Isle of Man but now it seems that you can buy them in bulk off eBay so probably not such an interesting background story to it after all!
Still 2 very interesting finds... I'm starting to amass a bit of a button collection!!