Why do rivers 'burst' their banks?

A common term is US usage is overflow

(especially of a liquid) flow over the brim of a receptacle:

[with object]: the river overflowed its banks

In many places, water is contained by dikes or levees and these are prone to bursting. Theses are more often lakes or inland seas than rivers, but some broad rivers are contained by levees. See this discussion of the Mississippi Levee System. Also a discussion of the Danube bursting its levees in Germany.

In those cases, the river may well burst its banks (fracture the levees). However, this may or may not apply to the rivers of England.

Might this be linked to the drainage of the English Fens? It was a project which was attempted on and off for centuries, but it involved the cutting of new channels (Wikipedia says that the old and new Bedford rivers were two prime examples) with raised banks, to stop the water from pouring back over the reclaimed lands. This project was largely completed by 1820, a few years after Peter Shor's quote. In this context a burst bank would be different to an overflowing river, as the quote implies, and would be an accurate description of what has happened.