While England is not generally thought of as a foodie scene, beyond bland food, pub fair, and fish and chips, I can definitely recommend some places to eat that I would revisit:
Bakeries & Tea:
Paul Bakery
Paul Bakery can be found as you round the steps of St. Paul Cathedral. I got a sandwich and a hot chocolate. It was here I learned that the British hot chocolate is essentially like drinking a melted chocolate bar. Luckily they know tourists aren’t used to it, so they’ll offer you a taste before you commit. I accepted their offer to lighten it with milk.
As I ate and stared at the steps of the cathedral, thinking that they looked familiar, a strain of music drifted into my mind, “Early each day to the steps of Saint Paul’s the little old bird woman comes…Feed the birds, tuppence a bag…” I recognized this spot thanks to the Marry Poppins film. As the film is based on the books, I’ll count this as a literary tie.
Konditor and Cook
We frequented this bakery almost every morning for breakfast pastries. The bakery is famous for little square cakes, which were used to make up a pixilated image of the Queen’s face for the Queen’s Diamond Jubillee.
Balthazar
On Sunday when Konditor and Cook didn’t open until 11am, we found ourselves in the theater district before finding a suitable patisserie. We found mouth-watering pastries at Balthazar Bakery. The shop being tiny, with few inside seats, we decided to carry our breakfast outside. We spotted an empty outdoor table and sat to eat to the sounds of an opera singer wailing away somewhere close by. Upon finishing my pain au chocolate I examined my surroundings. We were next to the Opera House and seated at Covent Garden East Colonnade Market. There were mobile stalls, indoor shops, and outdoor performers. Altogether, I thought it much nicer than the Borough Market. I spotted a Build-A-Bear shop and went in, lured by the bears in British Guard uniforms. I decided to buy a teddy bear shirt that says, “KEEP CALM AND LOVE LONDON.”
Twinings Tea Shop
We may have walked out of the shop with quite a few boxes of tea… But at least we would return home with real British tea!
Meals
Masters Super Fish
(Thanks to a recommendation found on Reddit). This was the first of many dinners of fish and chips.
Francesca
Italian pasta/café restaurant down the block from the Sherlock Holmes Museum. Choose your own pasta and sauce combination. 
Olivelli
Small Italian restaurant near our Roupell Street flat. This restaurant seemed to be an up and coming residential neighborhood with plenty of night life. Each of the pubs and restaurants had signs at the door politely asking that patrons leave quietly to respect the residential neighbors.
The George Pub at The George Inn
According to the website, the George Inn is London’s last remaining galleried inn. It also claims that Charles Dickens visited the site when it was a coffee house and he mentioned in Little Dorrit.
We had a very satisfactory lunch at the pub. Normal pub fair, burgers & fish and chips.
Greensmiths
Greensmiths is a a farm-to-table type grocery store and cafe. The first counter upon entering the shop was the butcher with his meat. This is where we lost Micah. He would have stayed there all day chatting with the butcher if we’d let him. At the back of the room were bread and pastries. The next room had 4 stories with a staircase down the middle. On the bottom floor I found dairy products, above that vegetables, then a half floor above that might have been drinks, and the top floor held a very small restaurant.
The kitchen used the locally sourced food from the shop for their dishes. The breakfast menu included a Full English Breakfast, and since we hadn’t had one of these yet, I retrieved Micah and we took a table. We started with glasses of apple and orange juice, which are pressed in-house. I’d never had freshly pressed apple juice before! The scrambled eggs were amazingly delicious. I’d been missing eggs for breakfast, which we have at home on the weekends, so these hit the spot.
Those croissants …yammy !!!