There is a lot of research that can be done on the history of tempi and the history of the metronome (which are not the same thing). (On the latter, I haven't read it, but can recommend the work of Alexander Bonus, who I've worked with. He's done some thinking about how the Industrial Revolution and machine age brought increasing standardization and mechanization of tempi. This seems like a "trailer" for his work.) Research is only going to get you so far, though.
You'll note that many of these indications tell you about factors other than tempo (and some might not even give you any clues about tempo at all). "Not too quickly? How the heck quickly is 'too quickly?'"
This is a familiar dilemma to the performer of any piece without a metronome marking (and even quite a few with them, which we might choose to doubt or ignore). "Lively?" "Soft?" "A bit more?" What are we supposed to do with these?
One answer is that often the music gives you its own clues. Sometimes I've gotten 3/4 of the way into a piece before discovering that the tempo I chose at the beginning was too fast. (I'm looking at you, John Eccles' divisions upon "John Come Kiss." Note, in that video, when the violinist enters, he takes a slower tempo than the lutenist offered. It's a bit sedate for the initial theme, but he knows what's coming at 2:00.
And the opposite is true; sometimes I've tried out something marked "Grave" and tried an extremely slow tempo, only to conclude that some later passage just didn't make sense that slow.
But the second answer is research. Choosing a tempo is a matter of performance practice, and as with all such questions, we want to get information that is as relevant as possible. 1928 UK practices are not the same as 1890 Italian practices. (See the kerfuffle surrounding the performance of one Italian in England in the form of Corelli's "Christmas Concerto": the discussion starting on page 14 of this pdf shows how hard it can be to reverse-engineer from the remarks of contemporaries what actually happened. In fact, that whole rather grumpy article is in response to generations of early-music practitioners either liberating tempi from Romantic anachronism, or (the author seems to imply) taking it too far.) In your case, you're fortunate because this publication is surely late enough that perhaps there are contemporary audio recordings of, if not these exact tunes, at least comparable ones. These might help you reconstruct a performance practice of Celtic tunes as received in the 1900s. (Though you might have to still factor in mechanical questions—does the process of recording and playback accurately replicate the tempo? Maybe...)
The plot thickens since these tunes are already decontextualized. You're asking the right question to ask "How were these performed in 1928," but all these markings were presumably superimposed on the tunes by whoever collated them. A completely separate question might be "how were these tunes performed in 1900," or 1850, or however far back they might go.