OK, call me crazy, but this is my take on your situation.
You will always be an American. It is not your fault, it is your birth country. Unfortunately there are prejudices out there in this world that may disinclude you from gaining friends in your British neighborhood.
How about starting an "American Dog Person in England" club? There may be other Yanks out there that need some friends too! You can put up posters in pet related retailers, groomers, vets, etc with your contact info! I bet you can pull some folks together for playdates, meetups, etc!
Honey, you know darn well that if I lived near you I would be AT YOUR HOUSE partying with you RIGHT NOW!!!
I am sorry that you are feeling a little down about this. Make some effort to make your own friends, and to heck with the snooty neighbors!!
Good luck, sweetie!
And rememeber, WE ARE HERE FOR YOU!