The book cites several other sources that are in agreement with its thesis (but claims they are not comprehensive enough). Care to cite the "mainstream linguistic opinion" that they were not
mutually intelligible? The link I provided was from a cursory search. I read another book arguing for mutual intelligibility but I have forgotten what it was (this was some 10 years ago). I found it very informative at the time as I wouldn't have guessed at the premise that Anglo-Saxons and "vikings" (not just raiders but also traders) were communicating with each other using their own respective language.
There is more to language names than the content and structure of language. Danish, Swedish, and Norwegian are still mutually intelligible, yet I think the speakers of those languages would take strong issue with someone wanting to lump each language under one name simply because they are mutually intelligible. Political boundaries, culture, even religion can call for a different name for a language.
Furthermore, it is well known that people alter their register
to facilitate communication, especially when speaking two differing varieties. If an American and a Scotsman are speaking, they each tend to avoid terms and sayings that are specific to their own variety that the other is unlikely to understand. The same goes for the Scandinavians: Word choice and grammar are carefully chosen so that the listener will understand.
The same concept applies to Old English versus Old Norse. It is quite possible to pick vocabulary and sentence structure using what we know of each language to produce phrases that are extremely similar to eachother. I don't think anyone is claiming that any
valid Old Norse sentence would be understood by Old English speakers and vice versa