If you only have one London breakfast, make it a full English at E. Pellicci in Bethnal Green, a family caff since 1900 with a listed wooden interior, where the Classic Set is £14.60. For the grand version, it's The English (£24.50) at The Wolseley on Piccadilly, served from 7am on weekdays in a 1920s former car showroom. If you need to eat before 7am, Andrew's and Beppe's open at 6:30am on weekdays, and Beigel Bake on Brick Lane is open 24 hours for a salt beef bagel.
A full English, for anyone who hasn't had one, is eggs, bacon, sausage, baked beans, grilled tomato and mushrooms with toast, often with black pudding (a blood sausage) and sometimes bubble and squeak (fried leftover potato and cabbage). The cheapest good ones are in the caffs, London's old-fashioned cafés, where a full English still costs about £10 to £15, and at some of them a mug of tea is included. Each card says when breakfast starts and where it stops, and names the nearest station on the Tube (the subway).
This page is about early, proper breakfasts. For late-morning weekend plates like pancakes and shakshuka, see the best brunch in London; for a flat white and a pastry, my London café guide. And if you're planning the rest of the day around breakfast, the best things to do in London covers the sights near each of these.