First of all I will assume that planning application was made and approved by the Local Authority.
Perhaps you should check.
As of the process, anyone likely to be affected should have been notified and asked for their views (if any).
If you were shown and signed as seeing plans that indicated that this area was a public open space and if the Title Deeds do not specifically permit Persimmon to change the plans you may have a case.
You could complain to Persimmon asking for them to stop building these houses or pay you compensation. When they object, you could make a claim using the Adjudication Scheme in the Consumer Code fro Home Builders.
Sadly, I am afraid as it stands in the current political climate, greedy house builders can cram as many new homes in as they can get away with (that people will still buy) and there is very little you can do other than rely on the planning process.
You should be thankful that, as far as you are aware, you may be one of those rare "lucky" Persimmon new home buyers with few issues, that is happy with their Persimmon home.