I don't drive in London, but it might be worth looking at parking at a Tube station on the outskirts of London and coming in by public transport. Parking can be difficult, expensive or plain old impossible - especially trying to get to the centre for an 8.30a appointment.
The embassy is within walking distance of Marble Arch (Central Line), Bond Street (Central and Jubilee Lines), Hyde Park Corner (Piccadilly Line) and Green Park (Jubilee, Piccadilly and Victoria Lines) Tube stations. It's about 10-15 minutes walking from any of those stations.