These are the tennis courts squeezed in behind the football ground Harvey end terrace and the Harvey Grammar School itself.
The first evidence I can find of these courts is in the 1931 Ordnance survey map, shown in the 1930-1960 section of the website, indicating "Tennis Grounds". The first photograph that I can find is from 1945, and is shown on this website on the same page. It appears to show grass courts at the Cheriton Road end of the row of tennis courts, and tarmac courts at the Polo Ground end of the courts. The tarmac courts are directly behind the Harvey end terrace of the football ground and highly likely that these courts have seen their fair share of footballs resulting from wayward shots in the football ground. Who goes in to collect the footballs?
The format appears to have remained the same for a considerable period of time. Here is a view of the grass courts in the early 1980s, with the Harvey Grammar School in the background (school main building to the left; library centre; science building to right) :-
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Picture credit; Mat Mackenzie
Recently the grass courts have been converted to 5-a-side football pitches:-.
Pictures credit: Google Maps
Personal recollection, and confirmation by multiple contacts indicates that the tennis courts are, and always have been, council owned. However there appears to be no information regarding the tennis courts on the council website.
The courts appear to have been used by many Harvey Grammar School boys during school breaks on an 'informal' basis over the years!