The closest you can get to Little Italy in the east.
The owners are amazing, the atmosphere is relaxed, the lunches are abundant and homemade.
The cakes are amazing, try Torta Clara (pear and chocolate) for the ultimate bliss.
There are not many places in London like it. On a Saturday during market hours it heaves with stalls and visitors for a good mile or two. Great place to pick up some bric-a-brac, genuine oddities and a great bite to eat, or just enjoy the hustle and bustle vibe of the place.
Also the Queens back garden, these beautiful grounds are great for a Sunday stroll to see the pelicans or to feed the squirrels. Duck Island Cottage is worth a look too, a idyllic little cottage situated in the grounds which was specially built as the bird keepers home.