"It seems to be the opposite where I live, but this is just for primaries, the only non denom school in the area (which is where my DCs go) attracts all the richer middle class families, as they tend to be aethists on the whole."
The overwhelming majority of richer families don't care that much about the denomination of the school, they are going on results.
If you look at the M20 postcode for example,
www.education.gov.uk/cgi-bin/schools/performance/group.pl?qtype=GR&f=n6X99FN8ft&superview=pri&view=&sort=l_schname&ord=asc
You've got
RC:
St Cuthberts RC 29% FSMs - undersubscribed by 3
St Catherines RC 8% FSMs - 194 applicants for 60 places, religious selection applied
Non-Denom:
Beaver Road 10% FSMs - 354 applicants for 90 places, catchment of 0.403 miles
Broad Oak 15% FSMs - fully subscribed
Cavendish Primary 21% FSMs - 214 applicants for 90 places, catchment of 0.698 miles
Ladybarn 40% FSMs - 139 applicants for 60 places, catchment of 0.633 miles
Old Moat 53% FSMs - (barely) fully subscribed - no catchment
CofE:
Didsbury CofE 7% FSMs - 205 applicants for 30 places, religious selection applied
St Pauls CofE 18% FSMs 148 applicants for 45 places, 0.405 mile catchment
The 3 most popular schools (St Catherines, Beaver Road and Didsbury C of E) are respectively Catholic, non-denom and CofE, and are within 1/4 of a mile of each other, in Didsbury, with FSMs of 8%, 10% and 7%. So there are basically three middle-class schools to choose between.
The next-most popular school, Cavendish is in West Didsbury, just outside the catchment for the posh schools in Didsbury, and having some overlap with the other schools, which are all in Withington (except Broad Oak which is sort of on its own to the south of Didsbury).
Within Withington, the least deprived school is religiously selective (St Pauls).
But when you've got a split where half (sometimes more) the schools are religious, it isn't possible for all of them to be selective. Religious selection enables financial selection, but it's not inevitable. A RC school in the middle of Moss Side is not going to attract the children of millionaires.
What religious selection does allow an over-subscribed school to do is exclude the poor, with very high success. It doesn't enable an undersubscribed, failing school to suddenly attract lots of middle-class kids.