Hello solittletime, open air swimming sounds great, we have a few returning expats from Singapore in our club who really miss it!
London has lots of clubs, small and large. The more inner city ones struggle with pool space using mixture of schools/local leisure centres with 25M so a weekly schedule may include lots of locations. Exposure to 50M pools is therefore limited for training, and being a member of the peripheral, larger clubs can be of benefit (e.g. Hillingdon, Wycombe, Guildford, Basildon...or South London clubs now using London Aquatic/Crystal Palace etc. I wasn't sure if it's West for definite you are heading for, or still flexible on location. Ealing's Gurnell pool is due for rebuild to a 50M (closes circa Sept 18 for opening 2020) as an example.
If your aim is longer term competitive for your children (normally from 9 here), look for clubs with a combination of teaching/development and performance squads where there's good progression opportunities.
Re swim coaches, London region does have good coaching, but I cannot vouch for each clubs' more junior coaches, and squad entry may be subject to capacity constraints (pool space, coach to swimmer ratios etc, speed of move ups), but most clubs' websites will have a PDF of their squad structures and minimum criteria. And how to apply, as some will have more regular assessments than others.
My suggestion, if you are really interested in the performance side is to play with the ASA tables, where you can see the clubs data within a set region, by age grouping, event times etc. This gives you a guide of how successful a club is vs the county/region/national clubs.
www.swimmingresults.org/12months/
Final tip - whilst your children are young now and it's easy to focus on Clubs nearer to where you (will) live, from 11 it may be easier for where they school (to go onto sessions if they are independent). The good news is that once your children start recording official times and if they have good basics of race principles/4 strokes, they are more attractive to other clubs making switch easier.
Sorry for the long waffle, hope this helps a little as a start point!