These rules, and landing in parks and so forth, were also discussed in the recent "circuits at unlicensed aerodromes" thread, in which there is some useful stuff buried amongst some criminally bad jokes perpetrated by me and some others.
Hyde Park etc, Regents Park, Hampstead Heath are themselves congested areas, because they are substantially used for recreation, and thus fall within the definition set out in the ANO. The Thames in central London is, similarly, a congested area, because it is substantially used for commerce and for recreation. Speaking for myself, I would not even contemplate flying single engined fixed wing over central London, but some people do it (didn't we discuss last year sightings of C150s over Hampstead etc?)