HEAVY RAIN, by The Spinners (of Liverpool, UK), is on their album "Best of the Spinners: Maggie May" (1998), and on the various-artists compilations "Folk Legends, Vol. 1" (2001) and "The Folk Box" (2002). According to Allmusic.com, on the last album, it is attributed to "Davis, Groves, Hall, Jones." Those would be the members of The Spinners. (Not to be confused with The Spinners of Philadelphia, USA.)

Here's what I was able to transcribe from a couple of samples:

Me no put no close-a-door,
So me no look when rain a-come-o.

Rain, rain, rain,
What a heavy rain and breeze!
Oh, what a heavy, heavy rain!
What a heavy rain and breezle [or "breeze-o"?]!


[Anybody know what kind of dialect is being represented here?]