Hi Akira
Have been doing a bit of further background reading today, as a lot of the Netherlandic history is also new to me, and it has in my own mind confirmed some of my thoughts towards your branch. The Spanish Inquisition was in Tourcoing in the 1580's, when Nicolas Pollet and his branch fled to Canterbury. I believe your branch probably did flee at that time too but in their case further up into the Netherlands, to the Protestant city strongholds there, i.e Antwerp, Bruges, Brussels.
I believe since Anthoine Pollet of Rotterdam has your branch arriving in Leige 1633, that they almost certainly went first to Brussels in the 1580's.
Between 1581-1648, the Netherlands gradually polarised into what would become the Catholic Spanish Netherlands (modern Belgium) in the South, and the Calvinist United Provinces (Modern Netherlands) in the north. This division was more or less clear by 1610, but not confirmed until 1648.
Brussels in the 1630's, though in the Catholic South, still held hopes of being part of the Calvinist north, and when the Spanish governess Isabella died in 1633, they tried to take advantage of the temporary vacuum of power, by seizing power in Brussels with Dutch Army backing. Apparantly Charles I of England 'accidently on purpose' tipped off the Spanish, and the Spanish troops on the ground were alerted to the plot. With this advantage they managed to contain the rebels into a stand off through most of the winter of 1633, before the King of Spains brother arrived the next year 1634 with 17,000 relief troops and put the rebellion down. Most of the Calvinists in Brussels would of course have faced dire repercussions for all this, probable execution as rebels, so a great deal who could would have fled, mostly north into Holland.
The civilians also suffered attacks, from both sides, that winter, I found this contemporary English report:
The English Resident at Brussels writes that the Spanish and Dutch armies remain without the one wishing to attack the other at a disadvantage, foraging and scouring the country. Strategic bombardment and attacks on civilians in Brussels reported. He adds that the approaching season will compel both of them to retire. London, the 7th October, 1633.
I think therefore your Pollets likely were amongst those Calvinists who fled Brussels in 1633 because of this.
I think it's also significant they later fled again from Leiden to England around 1668 (or some did at least), as this is exactly the same time Tourcoing was conquered by Louis XIV. Perhaps they orginally held hopes that at some point they could return to Tourcoing, but after 80 years in refuge, moving to Brussels, then again to Leiden, and now seeing their home town completely taken over by a foreign and hostile Catholic power, they had finally given up all hope of returning, and decided instead to join their relatives in Canterbury and London, concentrate on building a new life there. They do seem to have gone to Canterbury first before moving on a couple of years later to London.
Anyway yes certainly an interesting family, enough twists, turns and drama there to fill a book!
Regards
Richard