I've done a bit more research to check my theory and discovered that I was at least partially correct. The pair of semi-detached houses I've indicated were actually numbers 128 and 130 Claughton Road; Camden Lawn was number 130, so it's the left-hand one of the pair, not the right-hand one as I originally thought. Parkfield House is the next property along towards Charing Cross, at the end of the long curved drive.
My research also uncovered some more info on Camden Lawn's occupants. James Gamlin was elected a Birkenhead Councillor in 1891 and served as Mayor during 1899-1900. His wife Sarah Ann (née Furniss) is better known as Hilda Gamlin, writer of Memories, or the Chronicles of Birkenhead and 'Twixt Mersey and Dee, two popular volumes of local reminiscences. She was also apparently an accomplished singer and musician in her younger days. Unfortunately, she was of somewhat frail constitution, and sadly died at Camden Lawn on 2nd April 1898, her husband remarrying and surviving her by almost 25 years.
Camden Lawn was bought by the Corporation and demolished in the latter half of 1902 to make way for Claughton Road Special School, whilst number 128 had been bought by the Church of Wales as the site for their new Assembly Hall and was presumably demolished at the same time.