The current route goes through Brent twice. It looks like you need to stay a bit further North on the outer loop near Queensbury and Burnt Oak.
Edit: Alternatively, keep the outer loop and cross the Thames at Wandsworth Bridge and push the inner loop further South so you can go straight up the Fulham Rd to collect Kensington and Chelsea, and Westminster then a really tight loop through the Southernmost part of Camden, Islington and Hackney, quickly into Tower Hamlets and finish anywhere in the City.
The current route goes through Brent twice. It looks like you need to stay a bit further North on the outer loop near Queensbury and Burnt Oak.
Edit: Alternatively, keep the outer loop and cross the Thames at Wandsworth Bridge and push the inner loop further South so you can go straight up the Fulham Rd to collect Kensington and Chelsea, and Westminster then a really tight loop through the Southernmost part of Camden, Islington and Hackney, quickly into Tower Hamlets and finish anywhere in the City.