I've been reading through Michael Pye's new book, "The Edge of the World: A Cultural History of the North Sea and the Transformation of Europe." While he doesn't address the movement of herring directly, he does explain the growth of the Hansa (with a primary focus on how it relates to modern corporations). He makes special note of how important the annual herring markets in Scania, in southern Sweden, were to the economic power of the Hansa, and he does mention something important in an unrelated chapter: "until the world turned colder around 1300 sea fish also had their difficulties: neither herring nor cod like water to be too warm" (183). The Little Ice Age is generally thought to have lasted from 1300 to about 1850, and herring and cod moved south from the now overly-frigid waters of southern Scandinavia and the northern Netherlands to the more comfortable climate around England, Belgium, etc. The English fishermen were more than happy to cut out the Hanseatic merchants, who had controlled trade in the Channel for centuries.

More than the movement of herring though, Pye makes this point about the decline of the Hansa:

"In Amsterdam they now faced a major trading power, soon to be the greatest of them all, which seemed to see business quite differently from the simple force on which the Hansa relied. The Dutch talked about credit, which the Hansa resisted, and kept sophisticated double-entry books, which the Hansa adopted late; they could make trade abstract. The Hansa was going out of style before it went out of business" (240).

I don't know much about the Hanseatic League, and Pye's book is hugely wide-ranging, so he doesn't dig very deep into any one issue; this should get you started, but I'd suggest finding a source more focused on the decline of the Hansa.

*For anyone just getting to this, see below for /u/Enrico_Dandolo's comments on why the Medieval Warm Period and Little Ice Age aren't necessarily factors in the herring migration, or even real climatological events

From around year 1100 AD, the fishermen around Øresund began to catch gigantic amounts of herring when the herring migrated through the sound on their way to their spawning grounds in the Baltic. The herring bonanza lasted 300-400 years, during which large amounts of herring were exported to the rest of Denmark, Sweden and Germany. It is estimated that in good years, 200.000-300.000 barrels' worth of herring were caught in the sound. The herring trade was a major part of the region's economy, in large part due to the fact that herring consumption was allowed during Lent. During the 16th century the amounts of herring in Øresund fell sharply, but the cause of this is unknown. In addition to this, the reformation and the subsequent spread of Protestantism reduced the demand for herring.

Mostly translated from http://www.oresundsvand.dk/reports/diverse/fiskerapport.pdf and http://www.sildensdag.dk/silden/historie.htm)

Hugh Miller in his Victorian era book entitled "Scenes and Legends of Northern Scotland" talks a good deal about the rise and fall of the herring fishery in Cromarty, Scotland. The herring fishery boomed for many years (around 1700), until one year it dropped off completely, and the fish were not seen in commercial numbers for sixty years. Then it would revive itself on occasion, only to drop off again.

He said, "It is quite according to the nature of the herrings to resume their visits as suddenly and unexpectedly as they have broken them off, though not until a lapse of so many seasons, that the fishermen have ceased to watch for their appearance in their old haunts, or to provide the tackle necessary for the their capture; and in this way a number of years are sometimes suffered to pass after the return of the fish, ere the old trade is re-established."

What is interesting about Miller is that he was an early scientist, and he chides earlier generations for giving the loss of the fishery a supernatural cause.

Maybe you can ask /r/askscience or /r/biology ?