Right again, Alan....well mostly!
The steel screw sloop HMS Cadmus, launched 29th April 1903 was, I believe, the last ship to enter service with a figurehead. She was sold in 1921. Here she is, in all her glory.
Her sister ship, HMS Fantome, I believe to be the last RN ship with a figurehead (discounting HMS Victory). She was sold in 1925.
HMY (not HMS) Alexandra was completed in 1908 and also sold in 1925. I guess we can argue as to whether or not she was technically a Royal Navy ship - she was certainly crewed by the RN. She later served as a luxury Norwegian cruise vessel, Prins Olav and later still as a flagship of the Norwegian hurtigruten (Coastal Express) fleet.
HMS Alexandra was a broadside ironclad launched in 1875 and sold in 1908.
So, it's over to you to try and keep this going.
Rick