According to Wikipedia*, April is the driest month in the Netherlands, with only 41.6mm rainfall on average, as opposed to neighbouring months March (57.8mm) and May (59.3mm). This difference (about 40% more) cannot be explained by the extra day; that's only about 3%. The same thing happens (I suppose) for Belgium; the monthly averages for Brussels are 69.5 (March), 51.3 (April) and 65.1 (May). April is also the driest month in Luxembourg but not by that much.
*: you have to click the 'show' link next to Climate data for De Bilt (1981–2010 averages), all KNMI locations (1901–2019 extremes), snowy days: (1971–2000 averages).
While there must be a month in the year with the lowest rainfall, I wouldn't expect such a dip; all other months in the first half of the year are in the 60-70mm range (when February is adjusted for its short length). A possible reason for April to be the lowest is that sea and land temperatures are about equal, but somewhere in the fall that happens too, and that's the rainiest period of the year here.
As for other areas in western Europe: for England, April and May are about equal (56.1 vs 57.2). Hamburg, Germany exhibits the same behaviour as the Benelux.