If you were physically present in GA for more than 183 days, you are resident for tax purposes. As an aside, your right to vote in federal elections does not require residency or domicile - you do get the absentee ballot from the last state of residence/voter registration, but this cannot be used to determine that you are resident for tax purposes.
In any case - you need to establish a change of domicile. I did it in VA, which is one of the most difficult states for severing ties. It took me a year and a 2-inch thick pile of paper.
Generally, you need to give up your state driver's license, not have income from the state, sell your property (if any), not have kids in school who claim in-state tuition, not own or have a car registered in GA etc. If you maintain a bank account or US credit card, get the address changed to your UK address. Most banks allow this with no problem. Same with any other financial accounts - don't make the mistake of using a relative's address - use your address in the UK.
At this point you have moved to the UK, and unless you intend to return to GA, you have made the first step. This doesn't mean that you can't go back at some point in the future, but as of now, you are resident in the UK and have the intent to establish a domicile here. The best thing you can do is to write the Tax Commissioner in GA and ask what you need to do to apply for change of domicile. Most states have forms and a list of required documents. In can be done, but will likely require a high degree of tolerance for paperwork and dealing with bureaucrats in the appropriate state office.
