Once upon a time, this 14-acre park in Chintadripet was where M/s Burghall & Co., maintained their stables. There are a couple of references about the land being taken over, either by Simpson & Co, for expanding their carriage factory, or by the Corporation of Madras, for creating a park on the land. Of Burghall & Co themselves, little is known. There are a few clues in Robert Baikie's book, The Neilgherries, from which one makes out that Burghall & Co., were in the business of providing transit carriages: horse- or bullock-drawn, as you desire. Burghall's establishment seems to have gone belly-up in the mid-19th century, which was the time this park came into being.
It is possible that the park's creation was the work of both Simpsons and the Corporation of Madras. Maybe it was one of the first instances of the 'Open Space Reservation' at work. Whatever the genesis, Chintadripet's green lung was opened in 1869 and named after Francis Napier, the 10th Lord Napier, who was then Governor of Madras. Maybe because this park was slightly closer to the Fort than Peoples' Park, which was further northwest, it became a staging ground for meetings that were more political than social.
If I am correct, it was in 1990 that Napier's Park was renamed as the May Day Park. It is said that the first ever May Day rally in India, led by Singaravelar in 1923, was held near the Marina. Napier's Park is near enough, but there is nothing I have found to suggest it was the venue of Singaravelar's historic rally. The focal point for May Day rallies in these times is the Triumph of Labour statue on the Marina. The May Day park does see its share of gatherings, but it is certainly not primus. Could it be because this space to remember workers' rights is maintained by Simpson & Company?!
