Adding drainage wouldn't help much.
There's drainage in lordship rec and it's like a swamp.
Although it's frustrating to be unable to walk through flooded areas of parks, it's useful to remember that these places probably would have been built on last century if it wasn't for the fact that they flooded on a regular basis. So a bit of inconvenience every now and then is outweighed by the fact that we have these fantastic parks for the rest of the year.
I've always assumed the swampiness is partly due to the Moselle River being underground not too far away.
The road that links Belmont Rec to Westbury Avenue is named 'Lakefield Road'. On that basis the drainage is pretty good!