Ahh, with a bit of help from Google it came back. And with the health warning that this is on the basis of a casual conversation with a dad at County sports event and with another parent whose daughter moved to somewhere more academic for sixth form but was happy with the gentler, nurturing experience till then. The point was more that MN education conversation tends to be focussed around the selectives, in part because that selectivity causes such anguish. At times you can end up wondering how everyone has such genius children, but in reality this is not the case. And there are schools, The Hall in Wimbledon, St Augustines Priory in Ealing, St Dunstans in South London to name but three, which locals will know about and use and which some other children will commute a bit further to.
Anyway the North London school I was thinking of which seems to take less academic children was King Alfreds in Hampstead.
There will be others. And if the same pattern holds as does in the bits of London I know better, you may find the further out you go, the less selective and more inclusive schools become. And some may have bus services to cater for London children.
Also be aware that people can be quite sneery about less academic schools. It does not matter. What you want is the right school for the child.
You should engage the Head though. He is probably right in being cautious, some weird things happened this year, certainly in the bits I know. However he should have contacts and should try to sell the girl's strengths to suitable schools. Despite what appears on MN, not all children can be academic, and attributes such as kindness or emotional intelligence are equally important in adult life.
Good luck. We went through this at 11+, with the Head saying out dyslexic DD could not cope with an academic secondary. In the end our DD got into a more academic school than predicted. She then started flying in the run up to GCSEs. The really important thing though was to keep her confidence up, in part through finding extra-curricular activities she was good at, and to be open minded about future options.