Nothing to do with your parking problem, but one thing that may enrich your visit to the area.
The Great Exhibition, that took place during Queen Victoria's reign (the Crystal Palace bulding), was held in Hyde Park (it only moved to the Crystal Palace area of London after the exhibition finished).
Prince Albert was heavily involved in the Great Exhibition, which was a great succes.
To try and make something more permanent to celebrate art, learning and education an area was created just South of Hyde park called Albertopolis.
A number of buildings were built, including the Albert Hall, the History museum, Science museum and V&A museum, plus the College of art, the College of Music and others.
These were all buit in the one area, with support from Prince Albert.
After he died the Albert Memorial was built opposite the Albert Hall.
More on Albertopolis here
http://www.inetours.com/England/London/pages/S _Kensington.html
http://en.wikipedia.org/wiki/Albertopolis