Although I live in Scotland now I was born in the Fens and grew up in rural Norfolk, with family there and in Cambridge still. We always joked that we were never accepted when we moved to Norfolk (not a great distance), but in fact once someone else moves into the area you are no longer the newcomer and slowly shuffle up the line. I don't think Cambridgeshire is any better or any worse than any other rural area. Your neighbours are all individuals and will be friendly or otherwise just as in town. Scotland is a bit more friendly than England in general and we have settled in here more quickly than my family did in Norfolk, but we have tried harder too.
One thing we didn't expect here is that everyone seems to be related, if only distantly, to everyone else. Something else is the grape vine - in town (where we had to live for a few years), the neighbours who know/speak about you live in houses up to perhaps 3 or 4 streets away, but round here people up to maybe 20 miles around have heard what you are doing almost before you know it yourself
. The numbers of people involved are probably fairly similar, they are just spread out over a much greater area. Everyone has binoculars, ostensibly to see what's going on in their fields from the kitchen window, but of course they are useful to see what everyone else is doing too - mostly in a nice way
and it can help if you get into any trouble.
If you move into your new home with the view that you will be acquiring new friends as well as new neighbours, you won't go wrong. Particularly around Peterborough, I don't think there can be many 'locals' left as the area has been filled already with people from London.