London with the Eurostar? 

If you have used your outbound/ inbound travel days, you need to take the Eurostar from Brussels and get normal tickets to the Belgian border. 

It’s true, but it is not specific to London, it the same for every destination outside the Netherlands.

Go to this website: https://grenstreinbus.be/ , get to the border with you own bike/railcard, cross the border, and from then (in Belgium) the journey begins again! 

All I want to say is that while there may be very few places where the train actually crosses the border, there are many more places where the train comes close to the border, and where you can hop on. 

Where in the Netherlands will you start?

Don't forget, you can travel all day, then get a night train. As long as your train departs before midnight, it only uses one travel day.
So you could easily get as far as the Mediterranean, the Balkans, Poland, Hungary etc. if you want to cover a long distance. Or Scotland or the Nordics.

You just need to buy a ticket to the border.