Not that that wasn't interesting, but it's pop history journalism, with all its pitfalls (melodramatic lines and catchy but gratuitous hooks, and overselling pretty much everything). All the issues the guy mentions have been discussed for decades, and the consensus stands in spite of them because, despite its problems, it remains the most likely location.
This "TV historian" fails to take into consideration other names associated with the battle, such as Dingesmere (cf. Thingwall, a few miles from Bromborough), or details such as Óláfr/Amlaíb sailing from there directly to Ireland, or the form in independent Welsh annals (Brune; and by the way, the overwhelming majority of early sources have only one <n> in the name). If the Bromborough theory "rests on the name alone" (which isn't even completely true, as I said), his alternative doesn't really rest on anything but his assumption that everybody must have taken the most direct route, as if other considerations couldn't apply (like, I don't know, two big armies manoeuvring, perhaps having to get supplies from Man, or trying to get the Welsh involved for political reasons, or looking for the support of northern and western Wirral's Norse settlers, or what have you). Also, the article tries to pass as "early sources" stuff that was written 200 years after the fact, but I wager that's just the Daily Mail being ****, not the historian's fault.
edit: also, Amlaíb mac Gofraid was warring against Amlaíb Cenncairech of Limerick as late as August 937. It's exceedingly likely that he sailed directly from there to the western shores of England, to join the Scottish and Cumbrian forces; the Battle of Brunanburh must have taken place around October 937, so there's not a lot of room for a long detour.