Moving to Texas

I left Georgia in 2007 to come to the UK and don't have any intention of returning to Georgia. My drivers license will expire in a few months and they've made it impossible to renew remotely and I can't be bothered to jump through all their hoops to show up in person (they require 2 financial statements with a Georgia address, which I wouldn't have). My mother still lives in GA, so I have some residual mail there, but most of my mail is sent to the UK (incl. my US bank account and investments) although one credit card is registered to my mother's address in Georgia.

My best friend now lives in Texas, and will let me "move in" with him. This has the natural benefit of moving my domicile to Texas (although I have never been to Texas). Can I simply let my Georgia driver's license expire, update my US Credit Card address to Texas, and register to vote in Texas (can be done via post), and not have to file Georgia taxes anymore?

No.

Right, perhaps I should have asked an open ended question. If my proposed path doesn't work, what changes to my proposal can you recommend?

If you have no intention of returning to Georgia, what is the benefit of your keeping your US license?

I'm not bothered about the GA license - but it's sometimes useful to have a US license. The point here isn't about getting another license, but if the actions I highlighted (i.e. not having a GA drivers license, or any financial activity registered in that state) would allow me to sever ties and re-domicile in Texas where there's not state income tax.

My question is; why are you still filing Georgia taxes? Are they a "domicile state". It sounds as if you are UK resident and unless you have income with some GA connection or they are one of the nasty domicile states you should be able to avoid state tax. The GA connections you have maintained don't help in that regard, but they should be relatively easy to sort out.

I found this information in a forum that made me believe I still need to file GA state taxes..

Georgia doesn't have a lot of case law or provide a lot of explanation of its residency rules. However, the statute defines a resident as a person who is a "legal resident" of the state on "income tax day," which is December 31, and provides for part-year resident status for people coming and going. The statute also provides that once a person has established legal residence n Georgia, he continues to be a resident "until the person shows to the satisfaction of the commissioner that he or she has become a legal resident or domiciliary of another state." Ga. Code Ann. § 48-7-1(10).
A change of domicile, or legal residence, generally requires all of three elements: (1) abandonment of the previous domicile; (2) moving to and residing in a new location; and (3) an intent to remain in the new location permanently or indefinitely. States generally consider a US citizen not to establish a new domicile in a foreign country, because they assume the individual intends to return to the US eventually. Until a new domicile is established in a different US state, the prior domicile continues even if the individual has severed his ties to that place. For a married individual, domicile is generally the place where the spouse and minor children, if any, reside.
Some states have special rules allowing a domiciliary (or "legal resident") to be treated as a nonresident for tax purposes under certain circumstances, such as absence for a minimum period of time, especially in a foreign country. California, New York and New Jersey are examples. Georgia law includes no such provision. An individual's legal residence in Georgia continues until the person has established a new domicile in another US state.
The individual in this case remains a Georgia resident for tax purposes. Georgia does conform to the foreign earned income exclusion (IRC Sec. 911), however.

It sounds as if you have to become a legal resident in another US state for GA to consider you no longer a GA tax resident. You might try to convince them that you are no longer liable to GA state tax because of your long term residence in the UK.......of course that might have UK tax consequences.....I don't know your current UK tax residency status. Also I bet TX will require you to actually reside in TX to become a resident. Having the documentation without the physical presence and then claiming to be a TX resident sounds like a very dangerous path to take.