The story about queen Wilhelmina is that she "accidentaly" came across an English ship while visiting Zeeland and that she boarded the ship with the intention to go to Vlissingen or Breskens, but that the captain of the ship could only bring her to England.
So was this really the case or was this a "fake" story?
While it was not Queen Wilhelmina's first choice to be evacuated to England, I would not go as far as to call it an accident either. The situation regarding her evacuation, as well as the evacuations of her family, senior members of the military staff, members of the cabinet and intelligence agents, was complex; initial plans had to be revised during the course of the invasion due to the complications created, not in the least because of the presence of Fallschirmjäger and Luftlandetruppen behind the lines and the local superiority of the Luftwaffe.
The first time the Queen and her family had to vacate their premises at Huis ten Bosch was when it became clear on the morning of the first day of the invasion, Friday May 10th, that there were Fallschirmjäger present in the woods in close proximity to Huis ten Bosch, which was situated outside of The Hague. As such it was decided by the overall Dutch commander, General Winkelman, that it was best to move the royal family to Paleis Noordeinde in The Hague proper^(1).
This new situation was tenable until the evening of Sunday May 12th, when reports reached General Winkelman that essential components of the main defensive lines were overrun (the Wons position in Friesland was taken sooner than expected, the Dutch army had failed to retake the advanced positions of the Grebbe line, and neither had they succeeded in recapturing vital bridges in Rotterdam, Dordrecht and Moerdijk)^(2). These tidings were brought to the Queen around 04.30 the next morning^(3). The Minister of Defense, Dijxhoorn, and other members of cabinet were of the opinion that the Queen had to evacuated while General Winkelman was of the opinion that such a thing would be disastrous for the already fragile morale of the Dutch troops.^(4) In the end (we do not know the exact reason, but it is likely the General did not wish to move against the wishes of the entire cabinet) Winkelman acquiesced to the cabinet's idea of evacuating the Queen as soon as possible, something the Queen herself was reluctant to do^(5). Instead, she indeed opted to move to the province of Zeeland in order to rule from there (in Zeeland French forces had linked up with components of the Dutch army) which she would later explain as an "poging Albert" (attempt Albert) a rather mysterious phrase until we realise that King Albert I of Belgium likewise had moved himself to the uninvaded portion of his country during the First World War in order to continue the struggle from there. The word attempt is also important, as it highlights that there was never any surety that this evacuation plan would work^(6).
On that Monday, the Queen was moved to Hoek van Holland with a small following (7 individuals) to board one of the British destroyers there, the Hereward. However, due to a strong presence of the Luftwaffe over Zeeland in combination with the presence of naval mines in the waters there (they were mapped and therefore navigable but it severely inhibited room for any necessary evasive maneuvers in case of an air attack) it was decided during the trip that it was too risky an affair to make landfall in Breskens, resulting in the decision to make way for Harwich in England instead; a decision that was also not solely the Hereward's captain's, but also that of the Queen and members of her following (including two naval advisors)^(7).
To conclude: while it was not the initial plan to sail for England, neither was it the initial plan to make way to Zeeland. Plans were continuously altered during the course of the war as circumstances made necessary. For the influence of some of these circumstances on the evacuation of the Princesses, see one of my earlier answers.
Sources
Note that all works of De Jong are available for free download (in Dutch) on the website of the Dutch Insitute for Studies on War, Holocaust and Genocide.