SEH Kelly is a clothing manufacturer (and horn button user) based in London. Their website includes two pages with some interesting images of the manufacture of horn buttons at the James Grove factory (see next entry).
http://www.sehkelly.com/makers/button-manufacturer-the-midlands/ and http://www.sehkelly.com/words/2013/12/rubble-pt-2/
James Grove and Sons still made buttons in Birmingham until they went into liquidation at the end of 2012. There would appear to be a successor company (second link).
A website called Make It British appears to have tried to revive James Grove...
Firmin and Sons could at one time have been called 'rivals' to Hammond Turner and Sons! The company has always been located in London and they made buttons for both sides in the American Civil War...
I am often contacted by metal detectorists who have found a button: the first page, listing button makers, is part of the brilliantly useful UK Detectorists Finds Database. Old Copper also has a good list of button makers. If you have found a hallmarked button, the third link will take you to a pdf listing historical hallmarks.
For help with military button identification
Identifying Royal Naval buttons (G&H is good for recent ones):
Metal detecting club button pages
If you have a button made by 'Buttons Ltd', there is some information about the company on this page.
Pear buttons don't usually have backmarks - this article has some very interesting information about the trade
If you have come to this page looking for a manufacturer/wholesale supplier of buttons, you could try London-based Jessica Buttons, and Thomas Firth offer a wide range of buttons: it's good to see their sample cards! DM Buttons specialises in fabric-covered buttons, as does Harlequin. Jones & Company is a family-owned firm, founded in Nottingham in 1909. 'Hook' is a name long associated with pearl buttons in Birmingham - see the last article in the section above: it's good to see that the company is still in business.
For button retailers, try Duttons, or the online shops of Italian Buttons or the Bead and Button Company
For second-hand buttons (or to use their examples to identify your button): their stock will change all the time, of course...
Button-making history in Birmingham.
Birmingham's Jewellery Quarter covers a great many of the street named in the Trade Directories and/or Factory Inspections in the 'History' section of this website. Its well worth a visit.