We've recently adopted a 2 year old Jack Russell cross, he's been with us for a about a week. Unfortunately we don't have any information about his past, only that he shouldn't be in a home with children under 8. We're a house of 4 adults.
For two days he was quiet and timid but then he started growling. With most the family members he's okay but occasionally growls for no apparent reason.
With me it's the worst. When I come into the room he seems happy to see me, wagging his tail and running up to me. He also tends to follow me around the room and will try and get my attention by snuggling into my hands or jumping up. If I'm sat down he with also lie in my lap on his back for me to scratch his belly. But while he's doing all this he growls almost constantly, whether I ignore him or stroke him or discipline him he doesn't stop.
Every now again he'll be quiet and playful but often he's growling at nothing. And at times it has escalated into barking and he has bit me before.
Any ideas why he's doing this and how I can deal with it, as he is a very well behaved dog in all other aspects.

There's a difference between a growl of appreciation, pleasure, or wish to play/get attention, and a warning growl. Because JRTs are small, their threatening growl won't sound a lot different, however. (I have a JRT.)

As for nipping, yes, JRTs are known for it, and not just with small children. I got mine at age 4 because she was a nipper, most likely. They are one of the most frequently abandoned dogs. In the 7 years I've had her, she has tried to nip the ankles of countless people (not 'dog people,' whom she recognizes), and succeeded with one. I was caught off guard because it was a frequent visitor. It will take HUGE patience and time to train her to not nip in a way that you feel is secure. It would take a book to tell you how. I would hire a good trainer to come to your house to teach you how, or buy a book. And it will require other people to practice on with her. For now you just have to keep her on a leash when people visit.

Any new pet needs constant attention so anxiety of being left alone in a new place doesn't turn it into a neurotic mess. PLEASE make sure someone is with your dog all the time for a few weeks, at least, and be gradual about leaving him alone.