Found this old 78 at a boot sale today for 20p. It was recorded "Under the auspicesof the English Folk Dance and Song Society". Solo concertina. I didn't find much about Billy but a quote here about him sheds some light on his songs and his friends.
"Billy's concertina wasn't accepted by all in the side, either, being somewhat new-fangled (patented in 1844 by Sir Charles Wheatstone, though the “anglo” Billy played was probably based on a patent of 1884), but he could do Laudnum Bunches, The Blue-Eyed Stranger, Constant Billy, Country Garden, Rigs of Marlow, How D'Ye Do Sir, Bean Setting, Haste To The Wedding, Rodney, Trunkles, what some called Trunk Hose, and Draw Back. But the side's fiddler, Mark Cox, had gone off for a servant's job at Magdalen College up at Oxford, so they'd have to follow along of Merry Kimber's squeezebox, with young William Washington, the well-digger, him they called Sip, playing the fool. Youngest dancer'd be Charlie Massey, a brickmaker like his father, William, both of them known rather confusingly by the same nickname – Mac – then the two Coppocks, George, known as Spuggle, and George, known as Curly, the latter with great ambitions, later fulfilled, to have a load of men working for his building business, Billy's brother, Richard Kimber, known as Dobbin, making a great career for himself as a worker with the local district council, John Ward, known as Waggle (and you'd soon know why, if you saw him dancing), a labourer, Jim Hedges, known as Gran, a laundry delivery man, and the oldest man in the side, 54-year-old John Horwood, whose brickmaking trade gave him his nickname of Brickdust.