London's 350 acre Hyde Park has plenty of associations with dogs. There's a statue of Lord Byron and his Newfie 'Bosun' in the middle of Park Lane, and you can see the famous Victorian pet cemetery at the Victoria Gate entrance (but there's no public access).
There's outdoor seating at the Lido cafe, by the Serpentine.
Dogs aren't allowed in the hire boats at the Serpentine, but are allowed on the solar shuttle. (Closed in the winter)