Don't really consider any of this spoilers, it's just speculation.
My hunch will be that the professor will regenerate into saxon, jump into his tradis and disappear, heading to earth - Where he becomes saxon and runs for office. He can arrive at the earth much earlier than the doctor, hence all the vote saxon posters etc, that have shown up on the docs previous visits.
The doctor will need to arrive after the point in time when he last visited, to avoid issues similiar to the ones mentioned in the episode with Rose's dad.
Doctor will arrive just in time to stop Saxon from orchestrating a cue de tat. Saxon will have gotten an alien race to invade, as a pretext for him to seize power, Doc will have to fight them and prove Saxon is you know who