To be at loggerheads with someone...

The battle of Blore Heath, in the Wars of the Roses, was fought in Shropshire in 1459. As usual, Yorkshire won, they won all the battles except the ones that mattered. The outcome was that Richard III became king, but that belongs in the other thread.

Quite near Blore Heath (about 2 miles) is a place called Loggerheads- it's the nearest village, and the Lancastrian army would have marched through it, if not camped there for the night. The area supported the Lancastrians, so would probably have collected feudal levies on the way.

So did the phrase come from the battle?