Paul,
No mention in the London Gazette.
This was originally a partnership between William GREEN and George Thomas BAKER trading as Green & Baker at Albert Works, Branston Street, Birmingham, but as announced in the Birmingham Daily Post dated 3 September 1887, was disolved due to the retirement of William GREEN. However, I can find no mention of the firm in Birmingham prior to this date, possibly they traded elsewhere.
Throughout 1890 until 30 March 1905 George BAKER continued to trade under that name and regularly advertised in the Situations Vacant columns of the Birmingham Mail for staff, mainly young girls as solderers or youths for unspecified work, giving preference to those who had previously worked in the military button trade.
After that date I can find no reference to this firm, though it is possible that George BAKER died, retired, or went bankrupt. If I come across any additional information I will, of course, post it here.
Maurice