Eurostar high-speed trains are very popular and it’s extremely unlikely that seats suddenly appear. Someone might cancel its booking but seats will be gone in an hour. To worsen things : there is a passholder quota onboard those trains so regular tickets might still be on sale. It’s pretty unique in Europe. Those reservations are also one of the most expensive out there...
However don’t worry : there are loads of alternatives on that route.
Amsterdam - Bruges can easily be done reservation-free (and should be done that way to avoid paying a high fee!). Itinerary example :
- IC Amsterdam Centraal - Antwerpen-Berchem 09:28 - 11:23 (hourly)
- IC Antwerpen-Berchem - Gent-Sint-Pieters 11:42 - 12:33 (3 hourly trains)
- IC Gent-Sint-Pieters - Bruges 12:38 - 13:01 (4 hourly trains)
Half an hour longer if you prefer a single change in Brussels.
Except Eurostar trains all trains in Belgium and the Netherlands do not have reservations. Simply log the train you’d like to take before boarding, hop on and sit wherever you want (train ends are generally less busy).
Let me check for Paris - Amsterdam and Lille/Brussels - London, I’ll edit below. Feel free to check for yourself here (clearer overview) : https://www.b-europe.com/EN/Booking/Pass#TravelWish
1st January : Paris - Amsterdam
- direct Eurostar trains at 08:07, 15:22, 16:25 and later (32€ mandatory reservation)
For the convenience I’d rather get a direct train.
5th January : Bruges - London via Lille. For example :
- IC Bruges - Kortrijk 08:16 - 09:05
- IC Kortrijk - Lille-Flandres 09:14 - 09:51
- walk 5 min to Lille-Europe, passport controls
- Eurostar Lille-Europe - London St. Pancras 11:35 - 11:57 (30€)
About the same time via Brussels (08:31 departure instead). You can choose !
Questions welcome. Do not wait to book those 2 high-speed trains. Use B-Europe (Belgian Railways) : 4€ fee per order, compared to 2€ per person per train on eurail.com. Full flexibility on the rest ! :)