map

Kenilworth Court can be found on the Lower Richmond Road, near Putney Bridge, right next to the River Thames in south-west London, as you'll see from the map below. It's actually large enough to have 4 postcodes all to itself! SW15 1EN, SW15 1EW, SW15 1HA, and SW15 1HB! Putney itself is a thriving town, with good shopping and transport links and a wide range of pubs, restaurants and bars. Putney Bridge tube station, on the Wimbledon branch of the District line, is a 6 minute walk away. Putney main line railway station, with regular services into London Waterloo, is about five minutes walk up the High Street.
Many bus routes also stop nearby. The 22 bus from Putney to Piccadilly, stops right outside the court, while the number 14, to Tottenham Court Road/Oxford Street, stops on Putney Bridge. Other bus services from the bridge include the 74 to Baker Street via Earl's Court, the 85 to Kingston, the 93 to Cheam via Wimbledon and Morden, the 220 to Harlesden via Hammersmith, Shepherd's Bush and White City, the 270 to Mitcham via Tooting and the 265 to Tolworth. Right - a sadly-missed "Routemaster" double-decker on the 22 route from Piccadilly to Putney Common.
There's even a regular daily riverboat commuter service from Putney Pier on weekdays.

Map of Putney, showing the location of Kenilworth Court (red arrow).