As you may now, I have just moved into a local village just outside of Cambridge. Now village life is different from city life even in the UK.
The chances are you are going to be bumping into the same people over and over again so you have tailor your approach to getting to know people.
One thing that I suggest is keeping an eye out for local events. For instance, my village has a local fun fare on the village green this week. Next week is a bake off and there are other ones that come up over the year. Go to them, people are often very friendly at these things- even the British! I can only say that because I am married to one. For some reason, in these circumstances they feel more free to chat to people they don't know so it might be okay to talk to people in lines here but not at the line at the bank. Not sure what but that is the way it is.
The second thing is to use your local shops. Save yourself time, gas and sometimes money by shopping in your local shops. It is good to support the local communities as it gives a good impression of the American presence in the area and it helps to keep the things open that you love. Also in my own opinion, I think that the vegetables and meat are way better than anything you get on base at the commissionary. I am a "cook from scratch" kind of girl but the British call it just cooking so no readymade meals or Hamburger Helper for me, you can make your own. Also it gets you a bit more engrained in the local area instead of hugging to the Little America.
The third thing you can do is volunteer. A few weeks ago I heard that one of the Rainbow (Girl Guides = Girl Scouts) packs were going to have to close if they did not get leaders to take over. I am already a Brownie leader in the village over from mine. I would hate to see it close so I have told them that I would fit it in. You might be able to help your village out with something like this. Then you get to know a few people. One of the girls lives on my road and her dad works with my husband.
I have a dog and for whatever reason people will talk to you more if you have a dog than if you don't. I am not sure why but even when walking in Cambridge strangers would stop me all of the time but I guess that is the life of a golden retriever owner! I walk Dusty in the morning and in the afternoon and we are always talking to people. So I suggest walking your dog regularly and meet people.
Give it a chance. I know it takes a long time to fit in. I belonged to my sailing club for 3 years before I felt like one of the gang so I am going to assume that this will be the same. The good thing about being an American is that we are naturally warm and friendly and that can work to your advantage. The British will go at their own pace to getting to know you, but once they do, you will not be able to get rid of them!
Put your face out there :)
American to Britain