London is a park paradise. In central London there the Royal Parks (Green, St James and Hyde), small parks and countless squares. To the north you find Hampstead Health and to the south Clapham, Wandsworth and Tooting Bec Commons. And many more greenspaces.
The massive downside of London is that restaurants do not allow dogs with few exceptions. I have found these two websites particularly helpful with finding the exceptions.
Fritz and I ate at Andrew Edmunds with two of my friends. They thought it was a bit overpriced and variable, but I thought it was a cosy and good place. The menu is typical of British-French fusion and the wine list was extensive. You have to ring ahead to book, especially if you have a dog – there is a special book (by the window) where they put you.
There are alternatives to restaurants, of course! I have never had trouble walking into a café with Fritz and ordering food and a coffee to take away (to a park). Pubs are also a good choice and quintessentially English (even if you don’t drink). Pubs by parks are especially nice. Notes also let me bring him in. Fritz and I took a nice walk along South Bank, down to Gabriel’s Wharf. There are tonnes of outdoor food options.
The Angel & Crown on St Martin’s Lane off of Trafalgar Square is also a good choice. Generally, central London pubs are a bit grim, but this one has a nice atmosphere with a fantastic location. They also serve Otter Ale, which comes from the West Country. That in itself is a reason to go there.