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For what’s it’s worth the 2 speed in flat London is perfect, and even around the outskirts as it’s very doable (even dad-bods can do it).
Granted as everyone as the 2 speed is external and in very horrible conditions the derailleur does stop working to do crap on the roads. But a little wash after the ride it will be good as new.
With a 2 speed I would recommend to up the 50T chainring to 54T, you’ll appreciate this when your on the flat and not spinning out.
Biggest sensible cost saving weight saying if you want to go down that route would be saddle, seatpost, pedals and tyres. I wouldn’t bother with cranks as stock is pretty decent unless you want shorter cranks.
You’ll defiantly notice the difference once you change these parts and it does make it a little rocket ship at the lights.
Wouldn't it be cheaper/simpler to run it as a 3sp considering you've already got the BWR hub/wheel? That's how I've got mine setup and it's been grand.