Hi aj_sp_007
It costs more for most rooms up north, never mind London.
I think you will be lucky, or cold and damp with horrible housemates. You could also try
Timeout but the
cheapest on there is £55.
I just had a look on gumtree & someone wants to charge £50 a week for living in a garden shed in Wembley!
There is a also couch on offer for £25 a week, complete with
tatty quilt 
They are not ashamed that it doesn't even have a cover, just look at the picture they have posted.
I have been asleep dreaming nice dreams, and have now woken up to a world gone mad.