The song is modern, but indeed based on a real person. Although in many ways completely mad, Price did make one very important contribution to life as we know it today. From History Magazine: Cremation:

"One catalyst for the allowance of cremation in Britain was the 1883 decision of Dr. William Price of Llantrisant in Wales to cremate his son's remains. However, Price did this in full view of the public, creating outrage, and legal proceedings were taken against him. In February of the following year, the judge presiding over Dr. Price's case ruled that cremation was a legal procedure, provided that no nuisance was caused to others. Dr. Price went on to cremate his son's remains, which had been stored in his home during the trial, and Dr. Price himself was cremated when he died a few years later. Despite the ruling, only three cremations took place in England during 1885."