Step one:
Look around outside of Zones 1 and 2 (What?! The suburbs!!!) in little ol' IBS's. They still exist, here in Bromley I can think of four*. See what they have hanging from the rafters. (I've been popping into a few in the southeast for years now and picked up a few - a 653 Rourke/600 and a 531 Roberts-badged road frame (both awesome commuters) are my best-remembered finds, as much for the pennies as the ride)
Ignore the size issue. This is a project not a necessity. 2cm either way increases your options by many %. You will learn to love that size.
3 And ignore the genre - size, brand, country, condition, etc. Let the genre pick you. The frame that is right for you will guide you.
There is one - sorry I won't divulge -owned by a curmudgeonly fellow who keeps trading- and I can't see how - that has a few in and out over the year. His big windows help.
Utterly idiotic advice.