Just spotted your query. Pelham House School was a popular boys' prep. school which started in Bouverie Road, Folkestone. A new purpose built school was erected for Pelham House School in Coolinge Lane, Folkestone in 1894. It was designed by W H Seth Hughes for Edmund Stow Thompson who from the local directories was head of Pelham House School certainly up to 1902. From 1907/8 the directories give two Heads - TJF Haskell and Charles Edgington. The school was very up to date in its facilities and had a magnificent view overlooking the Channel next to one of the Martello Towers. It remained at the Coolinge Lane site until the 1914-18 War when its proximity to the Channel and the need for the military to take over the large buildings in Folkestone meant the school left the town. They never returned and the Coolinge Lane buildings were occupied after the war by St Stephens College, a Girls' school run by the Anglican nuns, St John Baptist, Clewer.
The building in Coolinge Lane remains as part of the Folkestone School for Girls, and is known as St Stephens.
The building in Bouverie Road was taken over by the County School for Girls in 1906 but in 1921 they moved into a larger building in Coolinge Lane, Praetoria House School, in 1921. This prep. school had also been evacuated in 1917 and like Pelham House school never returned to the town. This building was renamed Penfold House(Grade 2 listed) and is also on the site of the Folkestone School for Girls.
Hope this belatedly helps.