Lost Lorrenden by Mabel Esther Allan

Phoebe Lyndhurst has gone to boarding school since she was nine, spending holidays with her grandparents in London, while her parents work in South America. One rainy July, she falls in love with a painting at the National Gallery:

The picture was of an old, grey stone house, with twisted chimneys and mullioned windows. There was a terrace that dropped to a lawn and brilliant flower-beds, and in a corner under a tree a party of ladies was having tea.