As far as I am aware it Doesn't matter who owns or bought the car,If your G/F insures it with you as a named driver then in all intents and purposes this is perfectly Legal.
However if, comes a time for you too insure under your own name then you will not be able to claim for a no claims discount,as you were not the lead name on the previous insurance policy, hope this helps
P.S.
It may help to have a word with your local insurance agent