Hyde Park is bang in the middle of London's most expensive area. Moreover that area is notorious for its lack of cheap parking. It is rumoured that the value of a dedicated parking space in Knightsbridge is roughly equivalent to buying a house. There are plenty of commercial car parks (mostly underground ones), but they will charge a fair amount and probably won't take motor homes overnight - indeed many will not have the height clearance to get them in. There are loads of places to stay nearby. Unfortunately they will be very expensive. E.g. Hilton on Park Lane is right across the road from Hyde Park, but cheap it will not be. Further afield there will be cheaper places, though anything central is going to have a fair price tag.Probably best to find somewhere further out, and then travel in to Hyde Park on public transport, or cycle in if you don't mind traffic and unsympathetic drivers.