There is a building on Dover seafront that has a strongroom bearing this plate. (I don't mean to be obscure, but I'm not really at liberty to say which building). I did a bit of research and found that the Phoenix Iron Works partnership of Thomas Ismay and Samuel Richards Smyth was dissolved on 23rd May. 1866. Apparently the business was situated in Snargate Street.
It seems Smyth carried on as a sole proprietor using the existing company name.
Looking at the picture of the bridge at Fort Burgoyne and knowing the fort was built between 1861 and 1868 ...... well, it's anyone's guess, but the bridge appears to be an original fitting.