Eurostar Rotterdam to London question

In a sane world the time between trains in Brussels would be 10 minutes, the transfer cross platform, and the passport control would be done on the train. Unfortunately the UK has not had a sane government for decades...

In this case after getting of the train in Brussels you will head for the Eurostar terminal, will have to "check in" and pass through passport control. 1h45 is enough time for that. In fact, that will be long enough to get terribly bored, as there is not much but sit on a chair once through passport control...

I would have taken a flight in your case.

Thank you for the quick response. We are actually doing an Iceland cruise round trip from Rotterdam. And the train station is a short tram ride from the cruise port. We didn’t want to have to deal with traveling to airport, well in advance, checking luggage, or concerned about size of carryon, hoping flight is not delayed or cancelled, then getting to London and then having to get on long Piccadilly line & connecting (or ridiculously priced Heathrow Exp) into Victoria. So going on train to St Pancras and catching the Underground to Victoria, eliminates a lot of hassle.

So we did have some logic in our decision. Eurostar in Standard Premier is $142USD/pp. and about $10 for tram and Underground.

In a sane world it would be a direct train from Rotterdam to London with passports being checked onboard.

But it is what it is, and I don't see any issues with that much time between trains. Apart from maybe that you might get a bit bored. It's enough time to go through security and maybe buy some chocolate or beer as well. I would not consider flying, despite the change in Brussels.

@WengenK's comments about a sane government in the UK are not fair.
The UK is fully entitled to defend its border as is any other independent country.
There are lots of external borders to the EU or the Schengen Zone where border agents board trains for passport checks and hold the train while that check happens. Or the trains from Bucharest to Turkey where everyone is turfed off at the border at 2am.
Even on the International Trains from the US to Canada it is not a check on the move.
When the train is on the move is too late to catch someone who shouldn't be there.

There currently is a direct train from Amsterdam to London. But the Amsterdam station is undergoing a major expansion and renovation that will first impact Eurostar. So the direct train is being suspended for about a year.

As you buy your Eurostar ticket, or a few days before the trip, please check on the Eurostar website for their required pre-departure arrival time, both in Brussels and at St. Pancras. In many recent years (including the Pandemic, and Brexit ... ) it has been (in black and white I mean, I didn't travel on it recently) stated as much as 90 minutes. There have been many reports here, of patrons arriving only 30 minutes before the physical train departure (I don't mean necessarily in Brussels in particular) and being refused entry.

It's not my intention to make you more nervous, especially because you say you have 1:45 available, which is enough. I'm just saying that there is a formal, official answer to your question, which you should look up, to be sure.

You should also start writing (I mean in your personal itinerary, not fussing about newsboard etiquette!) "Brussels Midi/Zuid". There are nominally three stations in downtown Brussels, but only one has Eurostar departures to London.

I have put up another post today that Eurostar have now announced a further change of plan, and are providing booked connections from Amsterdam and Rotterdam across Brussels.
You can choose between a booked connection of 45 minutes and 1 hr 45 minutes, with the booking options amended accordingly today. Passport control is to be expedited for connecting passengers.
This supercedes the advice given by Tim above.

If you want to spend an extra hour at Brussels that is now your choice on a connection from Holland only, not on a journey originating from Brussels where the 90 minute check in still applies.
There is no minimum check in time at Rotterdam as you are joining a Paris bound Eurostar there.