The first thing to say is that I love the exclamation mark in the title. Its like an exclamation an Asterisk character would make ("By Zantium!").
Anyway, this is a frustrating read. The plot is fine; your basic Hartnell pure historical. The regulars get split up and the story then has four plot strands following their respective attempts to survive in ancient Rome. Nothing wrong with that, you can't beat a Hartnell historical. The setting also works, with enough jeopardy and unfamiliarity to keep things interesting. As a basic story this would easily have worked in the 60s as a 6 partner, no question.
Unfortunately the use of this template only serves to highlight the features of the book that simply do not work. The Hartnell era is now itself largely historical being over 40 years old. Its a measure of how brilliant the show was in those years that most of it holds up as excellent television to this day whilst most other television from the early 60s has been forgotten entirely. Hell even looking solely at Doctor Who, a story like The Aztecs feels less dated than Black Orchid.
But for all that there are still things the show wouldn't have done back in the 60s. It would not have had the Doctor observing/influencing the early days of the Christian religion. Indeed, you probably wouldn't have found many literary SF authors who would've done a story along those lines. Now it could be argued that the very function of the Past Doctor Adventures is to tell stories that could not have been done on the TV and that would be a valid point. The problem is that the situation isn't developed into a story. The Doctor clearly can't be seen as being a driving force in the creation of Christianity, partly because at this stage the Doctor "can't re-write history" partly because it would still be offensive to a great deal of the readership, but mainly because the idea is terribly crass. He can't be seen to openly dismissive of it for the same reason. So what we get is the Doctor fussing over some translations and making achingly bland PC speeches that say very little at every given opportunity. Seriously, its like Topping thought that the 1st Doctor's only words were the "wanderers in the fourth dimension", "citizen of the universe" and "one day I shall come back" speeches.
Ian and Vicki fare better in terms of their storylines. Ian is actually quite an interesting little political thriller. But both suffer with terrible characterisation. Ian and Barbara are, in reality, basically characters of the 50s. The "swinging 60s" hadn't really happened when they were in the show. It is therefore incredibly jarring to read and Ian who frequently reads like an Alfie/Parklife/Carry On film style of cockney geezer. To be fair its not like he is always out of character, but for at least half of the book he is. So the moments when he isn't out of character only serve to further highlight the many moments when Topping gets it frequently wrong!
Vicki gets an adequate plot, but is characterised like she has spent a couple of years living in Sunnydale rooming with Dawn Summers!
Barbara gets the best of the book. Her story is the strongest and the characterisation is the most authentic, albeit there are the occasional wobbles here and there.
So there you have it; a good story ruined by a hopelessly inaccurate depiction of the regulars.