Hello Mum to Be and huge congrats.
Antenatal courses do tend to get rather booked up I'm afraid. Did you have no luck with your local NCT branch? Could they not squeeze you in?
I run Better Birth Stories which predominantly teaches hypnobirthing with birth prep but I am now fully booked for our next course at the end of July. I will be running one at the end of August though which may work? Don't worry so much about dates, first babies do tend to arrive nearer the 41+3 mark so that would still give you time to make some friends and get some good preparation and practice done.
You can find the info at:
http://www.betterbirthstories.com
NCT used to or possibly still run Bump & Baby classes in SW11 which may be worth going to and if you put a post here to meet mums with September due dates you will get lots of replies. NVN also run regular meet-ups where you can get to know some other local parents and have a well earned coffee and some cake.
This is a very friendly area though and you will be amazed at the sheer amount of playgroups and classes which are aimed at mums with babies so you will get lots of opportunities to meet other people.
Melanie x