LONDON — J. M. W. Turner may not have been as naked in his appetites as his character was in Mike Leigh’s 2014 movie, “Mr. Turner,” but the British landscape painter certainly enjoyed life. Besides a London mansion, Turner kept a modest country house 10 miles southwest of the city in Twickenham that he designed, where he and his father relaxed, fished and entertained.

Turner sketched abundantly in the area and incorporated views of it in paintings like the giant “England: Richmond Hill, on the Prince Regent’s Birthday” (circa 1819), now at Tate Britain here.

Nearly two centuries later, the simple white country house that he named Sandycombe Lodge, a narrow two-story edifice with a gable roof and one-story wings, has fallen into disrepair. Water is seeping in, parts of the ceiling are collapsing, roof slates are loose and the basement has been damaged by flooding.

Now, with contributions and pledges from private donors and the government-run Heritage Lottery Fund, the house is about to undergo a yearlong renovation that will cost 2.4 million pounds, or about $3.5 million, according to the nonprofit Turner’s House Trust, the property’s owner and administrator. After the renovation the house will reopen as a tourist attraction.