Brant.....rent an ultra-wide (16-35 f2.8) and maybe a fast prime; e.g. Zeiss 25 f2.0 (great architectural lens).

Jet lag suggestion (used by airline crews); if you don't have an immediate obligation after landing, take a 2hr nap and then stay up as late as possible.

I would suggest, if possible, while in London....visit one of the universities.....we really enjoyed U. of Oxford and surrounding small towns. We also enjoyed the pubs in this area.....thatched roofed buildings, locals have their own mugs hanging up and walk in wearing their Wellies.

Hopefully you'll have adequate free time.

Bill