I have considered some of the schools on you list, have friends with DC who attended and have visited and enquired whilst helping others too. In the end my own DC went to central London preps, but I can tell you what I know.
HH- A friend had her DS there, but never recommended it for us, she also did not send her younger DS there. She did not say anything bad about the school, but her older DS ended up at one of the top 5 boys boarding regardless.
Summerfields/Ladgrove/The Pilgrims - big feeders to Eton/WinColl. Pay lip service about taking clever DC, but they mean gifted if you are not rich. I mention as I helped a few DC apply - did not get in, but ended up on Westminster/Winchester scholarships later.
Cothill House - recommended by a parent whose DS ended up at Harrow.
Dragon/Sunningdale/Papplewick/Aldro - all have been recommended to me by former parents.
I mention these things as for me, a diverse environment is important (and a bit hard to find outside London or big cities).
Good luck