The good news is, it works better than ...City of the Saved. It moves along pretty well and it doesn't rely on you being a Who fan. The bad news is, it's more or less a pulp SF novel of the Golden Age: lots of scenery, lots of events, no characters to speak of.
Marcus Americanius Scriptor is born into an alternate Roman Empire, two millennia young and still going strong. The entire Earth is Roman, peaceful, and prosperous (though the historically Roman form of slavery continues). Marcus is settling down to a life as a literary dilettante when he comes across an anomaly: a bracelet dropped by an old man who materialized in the Forum one fine day. Marcus grabs the man as he attempts to dematerialize again, and... zap. Welcome to a different alternate Roman Empire.
We follow our protagonist (viewpoint person, anyhow) as he starts setting up a timeline-spanning meta-Empire of Rome -- on behalf of his own world, which is of course the best Rome. This goes great, until he runs into a timeline-spanning meta-Third-Reich. And then there's some trouble.
As a high concept, this is terrific stuff. As a novel, it's not much of one. Lots of events, as I said, but Marcus might as well be a faceless passive voice. The closest he gets to coming alive is in his (first) experience of London's fall, dodging the Blitz, where he meets a doppelganger of his Celtic wife. This storyline is rapidly handwaved away in an unconvincing three-way, and Marcus goes back to didactically narrating war history. He loves Rome, and that's about all there is to him. He's got some historically appropriate blind spots (see slavery) but the story doesn't do anything with them.
The Nazis consolidate with the aid of another timeline traveller; a Roman homeworld is invaded; the Romans consolidate back with the aid of yet another timeline traveller; they kick some Nazi ass. Time-travelling gods show up and Marcus manages to make them hesitate, if not blink. That's pretty much it. Marcus writes his memoir. The end.
We get rather a lot of clever references. We get the requisite hints of canon and Paradox lore. (The original traveller is described as the eighth of thirteen fugitives. And then there's the War, unseen but far vaster than the petty struggle between thousands of Roman timelines and thousands of Nazi ones.) It's fun, but it can't make the book. The author goes big, but he doesn't manage to make it weigh much.