Taxi/Uber in London

Can’t comment on the second part but legally you don’t need a car seat in a taxi, you could just install it without the base though :)

I have a doona pram for that exact reason. Easy to take my own car seat

We used ubers a lot in London with my first (was during tail-end of the pandemic) - there's some useful guidance here https://www.uber.com/en-GB/blog/uber-with-kids-guidelines/

I've never taken a baby in a black cab but I think you can just take the buggy on. Depending on your journey though I would think about public transport - you can journey plan on tfl.gov.uk and choose only step free options. Hope this helps!

Black cans generally do fit a whole pram, I’ve seen plenty of people with prams go to GOSH out of black cabs and take out fully loaded buggies/prams :) if you have an infant carrier that attaches to the buggy just strap it in with the belt :)

Black cabs can fit 2 buggies lol. No need for a carseat.

Thanks everyone. More just for quick runnings to my MIL for a 15 minute ride yet 1.5 hours on transport