“Whan that Aprill, with his shoures soote
The droghte of March hath perced to the roote.”
Not exactly the same thing but clearly Chaucer expected it to rain a lot in April back in 1390. The actual rhyming sentiment is first recorded as “Sweet April showers/Do spring May flowers", part of a folk poem recorded in 1610.
So Saturday’s drizzle has definitely been “normal” for a long time. And we can expect the promised flowers in two weeks.