In the period this photo was taken earnest Victorians would have been despatching missionairies to the far corners of the world keen for the 'savage' inhabitants to be introduced to the ways of European civilisation. They would no doubt have frowned on 'sacred fire-pits' or barabicu from which our modern word 'barbecue' is believed to derive. The OED cites the first recorded use of the word in the English language as being in 1697 by the British buccaneer William Dampier, and he presumably learnt it while visiting Caribbean Islands to bury his ill-gotten treasure.
Time has rolled on however and modern users of the Lawns are no longer satisfied with the civilised pleasures of the Sunday parade but prefer to hunker down around a sacred fire-pit and burn and consume compressed patties of animal flesh. Unfortunately this produces unsightly scorch marks on the grass, destroying the roots as well as the visible grass so that the grass takes many months to recover: as the participants would know if they had lawns of their own.
Although one hestitates to solicit authoritarian action when there is already so much in modern society there seems no alternative if the Lawns are to be retained as reasonably attractive open spaces available to all. Please sign the ePetition on the Council's website asking the Council & police to act against barbecues on the Hove Lawns.