After having a little think about where I have heard this type of sentence, I had a little poke around on the internet.

My Conclusion is.

Ignore everything on some internet dictionaries and word forums where this question seems apparently to originate from.

For a few specific places on the planet it might at a stretch be possible to refer to the "Rains" during a monsoon season but for your sentence rains is incorrect and a strange use of the word rains. As is pointed out by several senior members on these various forums.

the first sentence is wrong it should be rain and was to give the correct sentence which is the second one.

"it rains a lot in England" = plural it rains often and a lot

"it rained a lot in England yesterday" rained = there was rain in the past tense.

"it is raining hard today" = raining is now present tense.

"it will be raining hard/a lot tomorrow" = rain in future by word association with tomorrow and not strictly by grammar.

so we use rain, raining, rained for now and past

we use rains to describe that a lot of rain or frequent rain that falls at a certain time, at a certain place.

we do not say rains at a certain time or place when in either the past or future tense, but only in the making a statement tense.

"it rains in manchester more than any other place in England, so they say"

"it always rains when I go on holiday"

"it always rains in April in England"

"it rains continually most days in an English winter"

I hope you can see the pattern.

"it rained yesterday for 8 hours non stop"

"it rained every day during my holiday"

"it rained non stop in California I wish I picked a better week to go on holiday"

it was raining constantly for 8 hours yesterday"

"the rain did not stop for the full 8 hours we were there" (notice I did not say rains here)

if it did not stop it became a singular period of raining.

"it was raining every night that I went out during my holiday"

The two example you give are different. 'Rains' suggests that it rained multiple times. 'Rain' suggests that it was constant or just not worth going into detail to explain.

That's the noun we're dealing with. As a verb, rain and rains are never used interchangeably.

By the way, I recommend to everybody to listen and to read the novel "There will come soft rains" By Ray Bradbury.  

<a href="https://librivox.org/search?q=there%20will%20come%20soft%20rains%20&search_form=advanced" target="_blank">https://librivox.org/search?q=there%20will%20come%20soft%20rains%20&search_form=advanced</a>;

<a href="https://www.btboces.org/Downloads/7_There%20Will%20Come%20Soft%20Rains%20by%20Ray%20Bradbury.pdf" target="_blank">https://www.btboces.org/Downloads/7_There%20Will%20Come%20Soft%20Rains%20by%20Ray%20Bradbury.pdf</a>;

Hello. Thank you, John, for a detailed explanation. 

There will come soft rains and the smell of the ground,

And swallows circling with their shimmering sound;

And frogs in the pool singing at night,

And wild plum trees in tremulous white;

Robins will wear their feathery fire,

Whistling their whims on a low fence-wire;

And not one will know of the war, not one

Will care at last when it is done.

Not one would mind, neither bird nor tree,

If mankind perished utterly;

And Spring herself when she woke at dawn

Would scarcely know that we were gone.

<em style="color: rgb(136, 136, 136);">Sara Teasdale</em>