Build your pizzeria website in London
There is no London pizza market. There are thirty-two of them, and your customers only live in one. A site that knows which borough it is in beats a site that announces it is in London, because the second one is competing with everybody and the first is competing with the four places on your road.
The catchment is smaller than you think
Ask someone in Walthamstow where they get pizza and they will name a street, not a city. Delivery radiuses here are measured in minutes of moped time, and a customer two miles away is a customer in a different borough with a different set of options. That sounds like a limitation. It is actually the only thing protecting you from the scale of the competition: you are not up against every pizzeria in London, only the ones inside your own small circle.
Which means the job of your website is narrow and winnable. Name the neighbourhood in the page title. State the streets you deliver to. Put the nearest station on the page. Those three lines do more for a London independent than any amount of general polish, because they answer the question the search engine is actually being asked, which is never “pizza” and always “pizza, here, now”.
Chains own the high street, not the street
Walk any London high street and the names repeat: the same three or four pizza brands, in the same units, with the same menu in Croydon as in Kentish Town. That uniformity is their operating model and it is also their ceiling. A branch cannot tell you who is on the pass tonight, or that the dough is slower in winter, or that it closes early on the Sunday of the carnival. It has nothing local to say because it is not from anywhere.
You are. Put that on the page in plain terms: how long you have been on the road, who makes the dough, what changed on the menu this month. It reads as confidence to a customer and as substance to a search engine, and neither of them can get it from the chain two doors down.
Start with one borough
If you have two sites in two boroughs, give each its own page with its own address, hours and map, under one domain. If you have one, resist the urge to write for the whole city. The page that wins Peckham is a page about Peckham.