Menfreya in the Morning by Victoria Holt

Menfreya in the Morning - Henrietta Delvaney is the lame daughter of a Member of Parliament.  They are neighbors of the Menfrey’s who lived at Menfreya and also owned No Man’s Island.  At 13, Harriet runs away to Menfreya and Gwennan Menfrey lets her hide in the uninhabited house on No Man’s Island.  Bevil Gwennan discovers Harriet and when she suggests that she would never marry, Bevil suggests that he might marry her.