Timelords are immortal, right? They also have the power to travel through space and time. So, theoretically, shouldn't the entire universe just be filled with billions and billions of Timelords at any one time?
The chance of meeting one would be pretty high, if not infinitely high. Then again, you don't really see that in the show from what I understand (I've not watched all that much of it). But then, if you're playing by the rules of the TV show, there is a 100% chance that coincidences would conspire to meet you with the doctor anyway, and assuming you're a good guy, you're unlikely to come out the situation harmed.
So yeah, I'd go with the key. Seems like a better deal no matter how the situation unfolds, and there's only so much you can do with £1,000,000 before you'd get bored of it.