The flat is a short walk from the Hammersmith tube station. From this station you can get on either the District line, which takes you to Victoria Station, Westminster, and Tower Hill, or you can get on the Piccadilly line for Piccadilly Circus, Leicester Square or Covent Garden. Great for seeing all the London tourist spots.
Near the flat, there are some pubs and restaurants along the Thames, less than a minute's walk away. There are also plenty of shops and eating spots at the Hammersmith station itself.
If you don't mind a little morning walk, I recommend walking to Gail's bakery at Brook Green. They have a fantastic selection of scones, croissants, muffins and other treats for your breakfast.