I haven't given up either. I think you're right about the weather vane. So if the house is NE facing the prevailing winds are easterly, ruling out Hants and West Sussex where they are from the south, otherwise pretty much the area a lot of us have been looking but also includes East Anglia and more, see
http://www.bbc.co.uk/schools/gcsebitesize/geography/weather_climate/climate_rev4.shtml
Re the bit I've bolded - no, I don't think so.
Firstly, I find that BBC page and map rather confusing. Based on my understanding of British weather, it's showing the characteristics of winds from each direction, and the zones in which each of them is most noticeably felt. What it doesn't show is that for most of the time most of the country is under the influence of more or less westerly winds, so that in most places trees that are exposed to strong winds will lean broadly eastwards. (Near coasts this might be different, as maximum exposure is often towards the sea and there can be onshore winds due to local variations in land and sea temperature as well as due to global air currents.)
Anyway, what I'm getting from No.12/12a is that we're looking at the NE face (never mind for now the question of whether this is front, back or side), the trees are mostly exposed to winds roughly from S or SW (it's hard to be precise), but on the day the photo was taken, the wind was approximately NW.
I think this is still consistent with Sussex and the Weald area - and being nearer the south coast than the west, it may be reasonable to think of the prevailing wind there being SW rather than W.
Arthur