The site is under threat. In March, the SouthBank Centre unveiled £100 million development plans to transform the Brutalist building and relocate the Skatepark. Jude Kelly, the centre's artistic director, proposed building a new skatepark nearby but this was opposed by skaters who say they value the improvised nature of the space under the arts centre's brutalist architecture.
The campaign to save the Skatepark has gathered pace, uniting the unlikely combination of the National Theatre, English Heritage and the skateboarding community. One interesting part of the campaign is the application by the campaign group Long Live Southbank to have the site given protected "village green" status under section 15(2) of the Commons Act 2006. Under this provision, anyone can apply to the commons registration authority to register land as a 'town or village green' if "a significant number of the inhabitants of any locality, or of any neighbourhood within a locality, have indulged as of right in lawful sports and pastimes on the land for a period of at least 20 years". The site seems, at first glance, to be far outside the the archetypal village green, but the High Court in March 2012 held that a tidal beach was capable of being a 'village green'. Ouseley J noted that section 15 is not limited to a "conceptually traditional green...The law has always been more concerned with the character of the use than with the physical characteristics of the land over which the usage occurred." (R (Newhaven Port and Properties Ltd) v East Sussex CC  3 WLR 709, 721).
In a separate legal development, Lambeth Council has approved the application by the campaigners to have the site listed as an "Asset of Community Value" under Part Three of the Localism Act 2011, making it a 'material consideration' when the planning authority hears the application for planning permission.
This is a fascinating example of how the law can offer some protection to a heritage site that has acquired cultural meaning not through architectural significance but through folklore, energy, youth, sound and passion.
[Interesting also to note the the Southbank site includes the Waterloo Sunset pavilion, named after song by the Kinks. And here's a link to one of their fitting songs: The Kinks - "Village Green Preservation Society".]