Sorry Putney did not work out either - I am sure many lurkers have been crossing their fingers for you, as I have done.
In addition to pursuing Radnor, I encourage you to call the registrars at several schools mentioned by posters on your other thread, if you find those schools relevant (perhaps Kew House, St Catherine's etc) in exactly a month from now. Most of the "action" - cascading waves of offers being rejected - happens in the first few days of March, just after state school offers are out, and just as independent deadlines expire.
When deciding how many offers to give, the registrars have guesstimated acceptance rates, and your hope is that at least one of them clearly under-offered and will be scrambling to reach their target admissions number. Many of their waitlisted DC will also have settled on another school (where they got a straight offer - independent or state), with the registrar suddenly rushing to contact people further and further down on the waiting list with, perhaps, moderate success.
Places also come up later in the spring: Some parents will pay a deposit on an independent that they are quite likely to later reject, to "buy time" - e.g. if hesitating between independent and state (say, a grammar or good comp) which can be held without any financial penalties until school starts - feeling they still "save" a fortune if they abandon their deposit. That's when you want the registrar to know that you are keen.
(Prep to 13 is another alternative, as several on the other thread said.)
Don't panic, and be patient. Best of luck! Now back to lurking...