Hello,
I would put your sword circa 1845-1860.
Firmin was at 153 Strand (amongst other addresses) from 1783 - 1894. "Firmin & Sons" would probably indicate a date between 1839-1879.
As has already been said your sword in an 1845 pattern blade. Wilkinson started the tradition of the brass "Proof" slug in about 1845 which was then copied by other manufacturers. I would also suggest that the sword was probably made by Mole's of Birmingham bassed on the proof slug design. The hinged flap on the guard was officially discontinued in 1852 but as swords were a private purchase for officers they had some room for personal choice and I have seen many post 1852 swords with the flap.
I would personally date you sword from circa 1845-1860
The name on the scabbard of E & W Seagrove is probably "Seagrove, Edwin & William" who traded from 22 & 23 Common Hard from 1852-1859 which would fit in with the approx age of your sword. If the scabbard is original to the blade then you can narrow the dates down. They were mainly a Naval Outfitters in Portsmouth so this may indicate a naval link or it could be that the sword/scabbard was purchased in a hurry before boarding a transport ship.
(Most of the dates for the makers above come from Swords for Sea Service by May & Annis. You can also find them on my website
www.oldswords.com)