Cumnor isn't co-ed. The boys school has been going for ages, the girls school is going to be formed from the take-over of Lodge school (previously co-ed up to 11). So two single sex schools on different sites requiring a 5 minute drive between the 2 of them.
The local co-ed options are St David's and Oakwood, the latter being Catholic though they do take non-Catholics. Caterham is an option but it is a bit of a hike from Purley and the A22 isn't always the easiest of roads in the morning.
St David's isn't academically selective, but does have a good set of teachers who are used to a range of abilities, and certainly the more able are pushed whilst the less able are supported. Good family feel, every child is known, good behaviour is the norm though every now and again there will be a challenging yeargroup. Facilities aren't as good as the single sex schools (Cumnor/Croydon High) which have science labs and swimming pools, but they do have a sports field and goign swimming at a local school. Most children go onto the local grammar or indie schools, usually with a few scholarships throughout the cohort.
Caterham is academically selective, and does operate an early warning system so you will be told at certain stages whether your child is likely to pass onto the next stage eg by end of year 4 you know whether your child will get into the senior school. I'm not sure how the move from preprep to prep goes, but I do know that they do lose pupils at the end of year 4/beginning of year 5. Majority of pupils go on to the senior school which seems to be doing well these days.
I don't know that much about Oakwood, but I know state school teachers who send their children there, so I assume that they are happy with it!
Er, there is also Reedham Park. Have never really looked into it as I'm dubious about any independent school that charges such low fees. About 110 pupils or so I believe.