The tennis courts are free to use privately, if you are a tennis trainer you have to book time with the council.
From The Council: The Tennis courts are free of charge for park users on a first come first serve basis as long as its for leisure.
From The Council: We however have instances where an organisation may want to book the courts, this is not deemed to be for leisure so we charge on such occasions.
There is also an excellent lawn tennis club just around the corner, this is a membership club and offer many facilities to young future Wimbledon winners. (click here for their website)