Agree with Jojo that it’s not so much that parents have single sex schools specifically in mind, more that the top performing schools tend to be single sex in your area ZebrA. Schools such as LEH, WHS, PHS, GHS, G&L, SPGS achieve well over 90% 9-7 grades at GCSE every year. The boys schools such as Hampton, KCS or SPS are the same. This is why people put DC through the hoopla of 11 plus. To put the difference bluntly, even an outstanding state school would be achieving 30% 9-7. I think the national average is below 20%.
The academic co- ed option in your area would be KGS. Or LU if that’s not too far.
But other, less competitive schools such as St Catherine’s still have a much higher “value added” so this is why they appeal. They get in the region 50-60% 9-7 grades and some obviously think this is worth paying for. Plus much smaller class sizes.
Tiffin Girls and Boys have thousands applying and the tutoring for those schools is a whole other business altogether.
Of course, children can and do vey well at any school but, because you are asking, this is just a perspective on why people put themselves through the 11 plus madness.