Hi London Rob,
Great that you are about to move to london. Richmond Park is fantastic for training rides - I live about 500m away so use it all the time. However it is not really going to help with your commute.
The 2 logical areas to live (nicer, generally lower probability of death, less chance of bike getting stolen etc) are just North of london around Hampstead or anywhere in the SW direction from London - includes Fulham, Putney, Chiswick, Hammersmith, Richmond. All nice places.