Probably one of the Earls of Shaftesbury.
My guess would be the 7th Earl of Shaftesbury - Anthony Ashley Cooper. He was a British Tory who lived from 1801 to 1885.
His chief claims to fame were his involvement in legislation to help the poor working classes. He was chiefly responsible for the 1842 Act which stopped women and children from working down the mines. He was a strong supporter of legislation to improve factory conditions, including the Ten Hours Act of 1847. He was also associated with the establishment of free education for the poor ( the "raggedy schools" ).
Of course, Shaftesbury House and Avenue could just as feasibly be named after one of the other Earls of Shaftesbury. ( Though probably not the first Earl because, although he was Lord Chancellor in 1672, he was accused of treason and fled to Holland. Not likely that the Establishment would name an avenue after him.)