These are not necessarily British, and "folk" is always debatable, but there are several threads about flood songs:

Origin: Galveston Flood
Lyr Add: The Sheel Raa Flood
Lyr Req: Night of the Johnstown Flood
Lyr Req: The Mississippi Flood
Lyr Req: Flood Blues (Sippie Wallace) + others
The Ohio River Flood of 1937-any songs?
Songs of Mississippi floods
Origins: By the Waters (Floods, Rivers) of Babylon
Lyr Req: Texas Flood (Larry Davis)

And I happened to find these additional songs that are in threads about other things:

THE PREACHER AND THE FLOOD (Joel Mabus)
FIVE FEET HIGH AND RISING (Johnny Cash)
HIGH WATER (FOR CHARLIE PATTON) (Bob Dylan)