Oh OP, I completely understand how you feel
It's just me and my autistic 5 year old girl
She's lucky to have you and her dad, as kids really need strong, sane and loving parents more than anything (be it, a single mum or dad or whoever is raising them)
Have you tried your local boroughs stay and play sessions - do they go up to that age?
I find them quite flexible, and if you explained your situation, I'm sure they'd let you take dd along, to get her into a routine of going outside
I think routine outings to low stress places is the best place to start, op
Perhaps you could have a routinely weekly shop, on weekday mornings (if you can swing an hour off work) where she goes to buy fruits and essentials? To the same shop at the same time. For us, every Friday we go to lidl so my girl can pick out a donut. Sounds weird but she likes it and now understands how the shopping process works
Perhaps you could take her to a local park, early on a Saturday morning (it's getting colder but could give you both some exercise. Our local one has a basketball court, so we'd go early before the big boys arrived)
Maybe you could go swimming weekly, again early on a weekend to avoid young people?
You're not alone op, lots of parents are like us, as I've found on mumsnet.
I've decided to embrace this winter and make sure we enjoy it. You can't help that you don't have any family. What you can do is make the best of life now.
For example, I put together a massive ball of gingerbread dough, and after school, my girl helps bake one gingerbread man a day for her lunch the next day.
Sorry for the long post 😅, I'm just in a similar boat and have felt the exact same as you. We are lucky that my girl has a sen school but it's still just us outside of it ❤️
Ps, you sound like a loving mum x