Sorry you have not been lucky in finding current parents. We discovered WHS when we were looking for 11+ alternatives for a sporty girl who struggled with English. I basically went through the Good Schools Guild and then put all the post codes into TfLs journey planner. Hence my interest in school demographics, as I tried to work out what was worth applying for. If we allowed a maximum of a 50 minute journey in any direction there were in excess of 25 girls and mixed indies we could consider.
WHS is surprising accessible from Central London, but not on the general radar. I assume people look at the tube map and forget that as long as you can get to Waterloo or Vauxhall there is a fast and frequent train service. (Or change at Clapham Junction from Olympia or Victoria). Wimbledon, for someone who had never been there and in contrast to Dulwich, is well connected to other parts of London including a train loop that goes through places like Clapham, or on the tram that potters through south London. Both my daughter and I thought it was a lovely school, and felt that Wimbledon would be a great place to meet up with friends outside school. (Unlike, say, City) .
Kings in contrast is well on the central London map. Indeed there has been surprise when new parents discover that the majority of pupils tend to come from further out of London. I suspect this represents the lack of indie alternatives for boys and the ferocious competition for what there is.
I understand (DD ended up unexpectedly getting her first choice school, one she had been advised not to bother to apply for, and like marriedinwhites daughter has continued to make progress) that with the appointment of an impressive new Head, WHS that year was a bulge year that year , and the first year that girls living in Wimbledon generally chose WHS over Putney if they had the choice. I would assume that as more central and West London boys go to Kings, and it is now often preferred over St Pauls because of the latter's tiger-schooling reputation, more of their sisters will consider WHS, with half an eye on transferring at sixth form.
There is always going to be some movement at sixth form, though I would be surprised that with interest from a wider catchment the numbers involved will be a problem. It is a chance for the school to take in bright girls from elsewhere, including marriedinwhite's daughter. And a chance for the girls to expand their social circles as they meet their friends new Kings contemporaries.