So far no-one has said that a 250w kit is actually capable of doing this.
Cycling around north of Romsey (where it is at least as hilly as the New Forest) I have found only one hill which defeats my 250W rear hub motor. That is Cow Drove Hill out of Kings Sombourne : I don't know how steep it is (no signs as it is a back road), but smaller cars struggle with it creeping up in low gear. I can barely walk up it pushing the bike!
I'm only beginning to walk properly again after about 2 years being crippled with an arthritic knee. This means that I can't add much muscle power, but find 250W perfectly adequate and managing most hills between 7 and 10MPH.