If I moved to London, (visited 5 years ago--saw thousands of commuters) and wanted a commuter bike, I would go here: https://www.condorcycles.com/pages/contact

Yes FENDERS. Maybe rack in the back for a trunk bag but I really like my Carradice for my work clothes and lunch. Tires wider than 23-25 perhaps, but make sure 28s will fit with plenty of room under the fenders. I think 28s need 50mm fenders.

A new bike! What fun!