Bessie Tarver's Book Light And Shade

A Memory of Southport.

My Grandmother, Bessie Tarver, wrote a book about her life from 1891-1919.
She mentions going to Southport, after her mother's death in 1897. She describes going to the pleasure fair and going to her friend's house, which was Sephton House, Princes Street, Southport. Her friend's name was Nellie. I don't have her surname. In 1904, Nellie still lived at Sephton House. It is described as having two large bays windows, with net curtains, a lovely garden with tennis courts. Would anybody know if this house is still standing?
I have tried various censuses, without success.