Also live in London and use public charging - looked into all these before owning an EV. Depends really on which chargers are local for you and what you are prepared to pay for convenience.
Source London - charge per minute (not per kw) and price includes a "parking fee" - they are bookable and offer 3 levels of "membership/pricing" - all of them are expensive (because they include a parking fee)
Ubitricity - lampposts mostly in resident bays that are NOT dedicated to EVs so often ICED and you may have to drive around to find an available one. Also quite slow (I only got about 2.3 kw per hour recently) so bets for overnight stops. PAYG price is 24p per kw. They do have "membership" rates of 19/16.2p but you have to buy their own metered cable (at either £299 or £399) to access these prices - so only viable if you do a high mileage and use them exclusively.
Polar - with the PLUS card (£7.85 per month) you get 12p per kw prices - if you use their app (Polar Instant) instead you get 18p prices. (Polar PLUS also gets you access to 15p rapid charging).
We also have all 3 available locally and we've gone for Polar Plus as our main charger and Ubitricity as a back up - so far used both and got on OKwith them. We have 3 Polar stations within a 10 minute walk and about 12 - 15 Ubitricity lampposts in the same radius - and 2 Source London.