IGC and Brown lists a C Gilbert, gun and rifle maker, of 33 Whittall St, Birmingham 1864-67.
The 'from Purdey's' moniker was used by several ex-Purdey craftsmen, including Frederick Beesley, William Evans and Henry Atkin. James Purdey didn't like it much. However, it was the truth and there is nothing illegal about stating that.
Given that the C Gilbert above was in Birmingham, I suspect it unlikely to be your man, since it was usual to apprentice and then practice in one city only. I also suspect that your C Gilbert is from the 1880s, since that was when the 'from Purdey's' became fashionable.
Tim