Support Worker for Autistic Adult

Hello everyone.  I would like to know of your experiences and contacts if you have any, for funding for a support worker for my 21 years old autistic son.  He hasn't been out of the house for nearly two years.  He was at a special school who took him out regularly (for a coffee, walk etc). Since leaving school at 19 he's fallen through the cracks and doesn't go anywhere. He won't go with 'mum' and there is no-one else who understands him.  I spoke to adult social care who said he wouldn't qualify for a support worker and it's up to me to find and fund one.  They said, if he doesn't need help at home and he's not in assisted living then he wouldn't qualify for any help.  He's not in education so his EHCP, I guess has now lapsed.  They said he can wash, get a drink etc. (that is if you count the four hours to get him into a shower - that is!) and they could not guarantee sending the same person (which he would not cope with at all).  I've checked and we would need about 4-6 hours per week and it is in excess of 20.00 per hour.  That is income that I could not find and was wondering if all local authorities are the same?  I am in Southampton.  I look after my elderly mother in the same house and he definitely needs a break and a new face to help him back into society.  Any thoughts anyone?  Thank you for reading the post.