Unfortunately (for I like the title) this book hasn't got much to do with Doctor Who and doesn't explain science very well.
I think the problem is that it's simply much too short to talk about any of its topics in great depth, and so the author often just tells us things without explaining why they are so, or how scientists came to think this or that. Then again, when he does explain something, I often feel talked down to, as when he says: "Now, you might wonder, if the consequences of relativity are true facts, then why don't we experience them every day of our lives?" Because we're incredibly slow compared to the speed of light, I thought, so they're incredibly small and we don't notice them. Two rhetorical questions later (in one of which he appeared to confuse mass and weight) he finally says just that.
As for Doctor Who, it's just the hook for the scientific topics: 'Doctor Who is about time travel, so let me tell you all I know about time travel. There are aliens in Doctor Who, so let me tell you all I know about aliens.' Apart from putting the time travel chapter first, it could have been called The Science of Star Trek without changing much of the content; especially when, at the beginning of the chapter on interstellar travel, he admits that this doesn't play a big role in Doctor Who, but adds that it does in other scifi series, films and books, so he's going to talk about it anyway. When he does mention Doctor Who, he makes mistakes that are to the fan what confusing weight and mass is to the physicist: "... the malevolent aliens ... who regularly clash with Doctor Who and many other science-fiction heroes" (... but the name is italicised anyway just to be confusing.) He claims that Tom Baker was one of his two favourite Doctors, and that "'Time Ladies' are never mentioned in Doctor Who." I wish to return my copy of City of Death on the grounds that it must be some sort of complex illusion and doesn't really exist.
It's only in the epilogue (8 pages) that he finally goes into some Who-specific things - but even there he quickly gets from chameleon circuits to stealth vessels, after having dismissed transdimensionality as almost certainly impossible, in one short paragraph, without explaining why.
In short, I was disappointed both as a fan of Doctor Who and as someone interested in what the author calls "pretty far-out physics".