Eurostar: 6 months (120 days), I believe.
DB: 3 months (91 days or some such).
Dont know about Thalys.
If you want to travel to Berlin and save money, youll probably be best off with a DB London Spezial rather than buying from Eurostar + Thalys + DB separately; this would mean waiting until a bit closer to date of travel as DB bookings open later than Eurostar.
London Spezial does mean you cant take Thalys from Brussels to Cologne as the BelgiumGermany border has to be crossed in a DB ICE train on that ticket.
You can enter dwell time when booking a ticket from DB, up to 48 hours I believe, so you might be able to get a 59 ticket (109 in First Class) from London all the way to Berlin that lets you stay two days in Cologne en route. (Price varies subject to availability of price quotas, similar to Advance tickets; for example I was only shown 159 FC tickets for a particular trip last spring despite looking at a couple of minutes past midnight on the first day the booking opened.)