No prep school can advertise as a feeder school for true grammar schools in the area. Entry is via ranked score in the 11+ exam alone. Prep schools may do preparation for the CEM 11+ test but you can do that yourself. The 11+ is mainly time pressured. Lots to answer in a short period of time. The verbal (English) skills required are very high - usually acquired through reading and understanding over a long period of time.
You will need to check out residency requirements for any Grammar Schools you are considering, as some may require you to be living in the area the year before you intend to start to be considered in the first round of offers.
Entry to independent schools varies - most have some form of entry exam, the standard required can vary though. The bottom line - and, therefore last person in - can be quite low as, to put it crudely, private schools need bums on seats to pay the bills. Did the prep school give you an indication of how many girls went on to your target school this year? You are questioning their assessment of your DD by asking the question whether you should come back or not. Do you have doubts about the school?
Nobody can give you cast iron guarantees. Your DD may have a meltdown at the time of entrance exams or may be under the weather. She may just have a bad day. It happens. The cohort she is up against may be super bright - or not - and her position is always relevant to the cohort. You need to investigate the alternatives too - the "what if" scenario. What if she doesn't get offered a place at X private school or z grammar school? What then?
But, the brief answer is, with caveats, no you don't need to go to a specific primary to gain entry to specific secondary schools. People diy for the 11+ and get their children through independent entry exams from "normal" state primaries.
(Crossed with Ken who was far more succinct!!)
Aren't the KE grammar schools completely super-selective, so, assuming that one is eligible for a state school place, address would only be relevant in a tie for a final place, or in determining waiting list position? Having said that, I'm not sure how you apply for a place at a state school (as opposed to registering a child to take the 11+), without a UK local authority to do it through?
Where address would be important, though, is determining which alternative state school you would qualify for, should the score in the 11+ turn out not to be what you need for a grammar school place.