Archbishop's Park
This park used to be the grounds of Lambeth Palace but has been a public park since 1901. In addition to the green space it provides, it contains a range of sports facilities (booking required, except for the cricket nets) and a playground.

This park used to be the grounds of Lambeth Palace but has been a public park since 1901. In addition to the green space it provides, it contains a range of sports facilities (booking required, except for the cricket nets) and a playground.
Check the official site before travelling; hours and prices can change.
More parks

Hampstead Heath
320 hectares of wild north London — swim the ponds in summer, climb Parliament Hill for the skyline.

Greenwich Park
Royal park with the Observatory at the top — best skyline view east of central.

Regent's Park
Queen Mary's rose garden in June. Primrose Hill at sunset, year-round.
Source: wikivoyage