Not all Gallifreyans are Time Lords
The new Doctor Who series breezes over a fact somewhat established in Classic Doctor Who - Not everyone from Gallifrey is a Time Lord.
Much like US Senators are Americans but not all Americans are US Senators. Time Lords are a handfull of Gallifreyans who achieve a level of learning and pass certain requirements who are then allowed into an elite brotherhood. In the episode 'The Deadly Assasin' the dialogue mentions a plebian class, implying not all Galifreyans are Time Lords.
It can also be implied from Classic Who that the ability to regenerate is not a genetic trait of Gallifreyans but a scientific achievement granted to Gallifreyans who become Time Lords. The fact that regeneration is a scientific achievement rather than a genetic gift is demonstrated in the episode 'The Five Doctors'. In that episode The Master, having run out of his 12 regenerations, is offered a fresh cycle by the Time Lords for his assistance.
I believe the clearest arguement for both of these theories is demonstrated by the character of The Doctor's grandaughter, Susan.
It is clear that Susan was a Gallifreyan but not a Time Lady like Romana or The Rani.
This could also explain some of the actions taken by the first Doctor.
The Doctor stole the TARDIS from his people and brought his grandaughter with him as he fled.
It has often been mentioned both in Classic and New Who that the Doctor is a lonely man. That he brings companions with him to help abate the loneliness. If Susan had the ability to regenerate she could have traveled with him forever.
However, the Doctor left her behind on a planet so she could make a life for herself. Probably, because he knew she would grow old traveling with him while he would regenerate and become younger watching her age and die. Something which the Doctor would not have been able to endure.