Looking for a place for my 6 year old and I

I am recently divorced and looking for a place to rent to accommodate me and my 6 year old son who attends AIS in Penge.
I mentioned pets as we have a Cornish Rex cat who is relocating to Belgium in September but he may have to stay with me for a month or so while his relocation is being arranged)
We also have a gold fish but that can be rehomed.
We are very clean and tidy, my son is pretty chilled out and obsessed with building rockets from Lego, Star Wars, space and Pokémon.
I'm a linguist and musician, I sing in one of London's busiest choirs and row on the choppy side of the Thames with GYC and WCIT. I have ASD (Asperger's)
I do not smoke, and drink occasionally
I understand that spare room may not be the best place to look with a child but one never knows what may turn up ....
My son would be staying with me in term times and half of long holidays. I am likely to be away on school holidays and some weekends.
Please feel free to ask if you have any questions.