The Muffin Man, famously known from the nursery rhyme, lives on Drury Lane in London. This rhyme dates back to at least 1820 and refers to a muffin vendor who sold English muffins and crumpets door-to-door in the Drury Lane area, which was a poor and notorious neighborhood in London's West End during that time. The Muffin Man likely carried his goods in a basket or baker's cart while ringing a bell to attract customers. Today, Drury Lane is a much nicer area with theaters and shops, but historically it was known for its poverty and crime.
There are also folklore and urban myths linking the Muffin Man to a darker story involving a figure named Frederic Thomas Lynwood, who was said to have lived on Drury Lane in the 16th century and was rumored to be a murderer, although this lacks historical evidence and is considered an urban legend.
In summary, according to the traditional rhyme and historical accounts, the Muffin Man lives on Drury Lane, London.