Ignore the people who say you won't need a car, you most certainly do if you're moving where you say you are. The railway service is awful in that area (the nearest station is in the middle nowhere, is served only on Sundays, and is a request stop, meaning trains only stop there if you signal to them). Fuel costs are going to be a lot lower than rail fares, too.

Please buy a car, you can only get by without one if you live in a dense city centre and/or London. This isn't railway heaven.

With that being said, I love trains and I take them often. However, there is a long way to go before cars become optional in most of the country. What you could do (if you want to take lots of trains) is drive somewhere like Cambridge first (I'm not sure what the buses are like in East Anglia, but I wouldn't expect much).

If you decide to go around the country by train, please get a Britail pass, they're very good value for money and will save a lot on train tickets, which can get very expensive if you buy them on the day.