Um, technically, there were pure-blooded romans. I mean, I see your point, but...
Roman people, pure blooded, were just Latin folk, so I would like to correct what I said earlier by saying that in order for you to find a pure-blooded roman, you would have to go off of the known latin DNA stuff. But Latium (Italy), the place that surrounded Rome were not citizens of Rome until rome conquered them. They were given a higher rank in the "peregrine" class because of their closeness to the Roman society. Other people were just "peregrines", for example, the Jews, a conquered people were not granted Roman citizenship, but rather were treated like dogs, so they would not be related in anyway to the Roman's. Same with the Britains, after being conquered, I'm sure some blood was mixed together, but a very small portion.
So, I think that it is possible to find a pure blooded roman, just that it would be very hard.