Fears events in People's Park are damaging grass
The park recently hosted the annual Battle of Flowers Funfair and the Portuguese Food Fair.
The constable said he had been assured by the parks & gardens team that the grass could "take it".
He said he had offered to meet members of Friends of People's Park after the summer events.
The organisation previously complained about the level of noise caused by the funfair.
The fair returned to the park in 2010 after rules to limit the amount of noise were agreed.