Statistical estimation of the demand function for most industrial, and many agricultural, products is inhibited by price fixing or price stabilizing arrangements which prevent observation of the full range of possible price-quantity combinations. In the period 1956 to 1961 the London butter market has illustrated how markedly price can fluctuate, when not subject to a stablizing agreement. In the period 1958 to 1961 estimates of retail sales of butter are available, and these permit the estimation of the demand for butter at retail. The time lag between production and consumption decisions means that there is no problem of identification. The present study uses weekly price and quantity information, and there is a serious problem of auto-correlation of the observations. The interesting story of the development of the London butter market in Tooley Street has been ignored. Rather, this study provides a brief description of the current working of the butter market, together with new estimates for the demand function for butter in the United Kingdom. Previous estimates of the United Kingdom price elasticity of demand for butter have been published by Brown as -.6, in 1954-58, by Stone as -.37 in 1921-38 and anonymously in Economic Trends as - .34. In this study the elasticity is estimated as -.46 when retail price exceeds 2/6 lb., and as -1.4 at 2/6 to 2/2 lb.