The pat answer is the first Sir Winston, but this is unlikely. Why would Lord and Lady Randolph Churchill name their son for a 17th century ancestor, and a fairly dubious one at that? No, it was someone more recent: his grandfather, John Winston, 7th Duke of Marlborough.
Was Winston Churchill's father a Lord? If so, how did he serve in the House of Commons? And did this continue even after he found he had to get out of town, so to speak, when he "incurred the displeasure of a great personage" A movie could be made. Ah, the Victorians.