I have stayed in this area on my 3 trips to London so far!
Take the tube to the Earls Court stop (one stop from Gloucester rd stop) and exit at the Earls Court Rd exit. Once you step out of the station you will see a main street filled with all types of restaurants, indian food, grocers, and Boots the chemist if you need. Make a Left outside the exit for the aforementioned portuguese restaurant Nandos (spicy chicken, etc) which is also next to Prime DVD rentals which has an internet cafe.
Earls Ct is also just 2 stops from South Kensington via the District line (green).
Don't miss Kensington High Street either! It is filled with great shops and also has restaurants, Marks and Spencer and a Whole Foods. There is a stop for that off the northbound district line (green) or the circle line (yellow).
If you need a larger grocery store, you can exit Earls Ct station at Warwick road and make a right and walk about 7 minutes and youll see Tesco on Cromwell road. (The main street you would cross to get to Tesco is Cromwell Road). High Street Kensington would be also accessible by walking another couple blocks up Warwick rd past Tesco.