By invoking "theory", you made the question very difficult to answer, because not only does the work have to account for English, it also has to be a theory. Which aspect is more important?
See p. 18 ff of the Cambridge grammar:
The primary goal of this grammar is to describe the grammatical
principles of Present day English rather than to defend or illustrate a
theory of grammar.
Compare that to Santorini & Kroch ch. 1:
This book is an introduction to generative grammar from a Chomskyan
The Cambridge grammar is more a description of English with some assumed theoretical subcurrents, whereas Santorini & Kroch (or, Koeneman & Zeijlstra Introducing syntax) is an introduction to a syntactic theory, exemplified via English. If you are most interested in theory, Santorini & Kroch or, Koeneman & Zeijlstra would be better because that's what those books are about; whereas as a description of Modern English, the Cambridge grammar would be better.