Now you have clarified, I think you will probably struggle to find the type of school you want in South Birmingham.
Colmore, Bournville Village, Harborne are all very large schools, on very small plots of land, and all three are highly competitive. Bournville also has a specific catchment, whereby you must live on specific streets to gain a place (and closer is easier because it's hugely oversubscribed).
Moor Green has been easy to get a place at until recently for obvious reasons- but Tappetytap's post shows how difficult it is to get a true picture of a school from its website, or even open day- it sounds as though the school has really turned it around and is doing well now.
Is it the University you need to get to daily? If you're looking at Moor Green catchment then you'll probably need to cycle.
I agree with previous poster's assessment of Tiverton- it's a lovely school, but in a student area, so many people don't actually know it exists! It's small too, so more personal.
I am confused by your talk of streaming though. You seem to be looking for least competitive, almost alternative type schools but worried about streaming. Could you clarify for me please?
There are a few Montessori nurseries, but nursery school only, no primaries. There is no Waldorf school in Birmingham. Did you mean the one in Stourbridge? There is no way you could use that but be at University every day, it just wouldn't work with Steiner-style education expectations.
Regarding independent schools (i.e. fee paying) Edgbaston Girls have a good amount of outdoor space, and they are directly next to the botanical gardens, I think they do quite a lot of outdoor stuff. Hallfield have Forest School with a wild area, they have an allotment style garden and chickens, and all year groups access them as part of the school day. They also have a lot of outdoor play, and are on huge grounds. Blue Coat also have large grounds, with plenty of outdoor games, but I'm not sure whether they have a forest school area.
These schools are highly competitive though, aimed at achieving places in selective secondary schools (edgbaston girls to a lesser extent) and that does not sound like what you want. St George's has Montessori nursery, small class sizes, and is very much aimed at nurturing the individual. Strongly Christian though!
Fees at independent schools in England are not at the same level as those in Spain. I think you will be shocked when you begin to investigate.
As previous posters have said- all schools in England have a Christian ethos. There are no secular schools, and day worship is an actual requirement in law.
However, that is interpreted in myriad ways, and schools are often sympathetic to the needs of their intake, so in an area where the intake is 99% Muslim, the religious content will be tailored to Islam rather than Christianity. RE as a curriculum subject is where children learn about multiple religions, and isn't opt-out. However, a parent can withdraw their child from daily worship if they wish... but in my experience this is isolating for the child (there isn't much for them to do when the whole school is in assembly together) and they miss out on announcements, celebration of achievements, etc etc.