I'm afraid the waiting lists kick off from birth so i suggest you get on it!!
My little girl goes to The Pavilion Montessori School in Teddington... they take children from 2.5years, up until they go to school. I know they have a pretty tight waiting list as it's super popular and also excellent. Your little one is still pretty young, so if you are after a preschool, I would highly recommend you drop them an email and get your little one on the waiting list - the website is
www.pavilionmontessori.co.uk
I also looked into primary school nurseries, but I was put off by the fact they have to be 3... and also that it's not possible to guarantee a place. The last position you want to be in is to have no pre school option, so if i were you i would put them down on 1 or 2 waiting lists at least then you won't end up with nothing. In Teddington, Children's House and Playwam are also great preschools i hear from friends.
Good luck!