When I was here as a visitor in 2012, I purchased a car from a private seller, registered it in my name to my now-husband's address, and insured it through USAA's London affiliate. I paid cash for the car, so there were no financing issues to worry about.
As far as I know, there was nothing untoward with what I did. DVLA had no issue with me being the registered keeper of the vehicle, and I was able to insure it.