If you ever want to go between Britain and The Netherlands this has to be the most relaxing way to travel. Get on the boat around dinner, eat dinner on the boat, have a beer, go to your room and sleep, wake up in your destination.
It's even better than night trains.
For booking, one has to be careful to book the inter-European distances from Brussels with a reduced price a bit in advance (for example from the German bahn.de web site). It's called Eurosparpreis or so. Also, for the British trains there are resellers which sell the seats much more expensive, so one has to watch out not to be short-changed.
By the way, another and often cheaper alternative is to take the ferry from Newcastle to Ijmuiden/NL which is a port of Amsterdam. As well as the Caledonian Sleeper, it leaves in the evening and arrives at breakfast time. And you have a nice two-people cabin which is a good place to sleep. It can be like 120 € per person for a return ticket.
https://www.dfds.com/en/passenger-ferries/ferry-crossings/fe...
Although since you mention using the Internet and also the Eurostar, you probably meant the day train, which is fine but the 6 hours to Berlin take a chunk out of your day. (I once took the one at 5 AM, but that turned out to be too early for me and I can't sleep in a chair.)
It's not quite as seamless as a direct train but still very enjoyable:
You take a train in the evening from London to the ferry terminal in Harwich, then overnight ferry in a private cabin (it's a big ferry with restaurant and bar etc.) to a port in southern Holland. Then a train from there to Amsterdam.
The train tickets are part of the ferry price (rail and sail) and you get into Amsterdam nice and early.
A trip I've done several times is London to Edinburgh. It's a quick flight and even a quick train during the day but if you want to spend Saturday and Sunday you'd have to get up early on Saturday to catch a plane or train which would get you in by noon.
Instead you take the Caledonian Sleeper on Friday evening and arrive in the morning in Edinburgh, ready to start the day.
Although you won't get the absolute best night's sleep, if you come prepared (sleeping mask + ear plugs) you'll get a very decent night's sleep (better than having to wake up early on Saturday).
It's also fun going to sleep and waking up somewhere different!