Historically, our Regiments have never been tactical entities; in the time of Wellington, a Gentleman might secure a contract with the Crown to raise, arm, clothe, equip train and field a Battalion for service against the Enemies of the Crown, and we later (in the 19th Century) tied pairs or threes of these entities to particular geographic areas for recruiting purposes, labelling themselves 1st, 2nd,3rd Bns of the Loamshires or whatever, but one would be acting as the Depot unit, pulling together and training drafts of soldiers to dispatch to the others, wherever they might be stationed arouythe Empire.How's that work then? We have multiple Field Armies, Corps, and Divisions before we get down to Brigade and Regiment sized elements.
In wartime, if it was necessary to field a tactical element of 4 battalions (equivalent to a US or Continental European regiment), we'd pull together the required number of battalions, paying no particular heed to capbadges, and call it a Brigade. Pretty much how we have rolled for the last 100years.
Somewhere in there you have the seeds of @old_fat_and_hairy 's discomfort.