How to travel from northern Germany to London by train

The connecting time between trains at Koln Hbf station will be around 53 min and trains from Hamburg very rarely arrive more than 45 mins late, so making the connection shouldn't be a problem.
Though it is not 100% guaranteed.

The connecting time between trains in Bruxelles will typically be around 1hr 20mins

Depart from Hamburg before 07:00 and you will be taking an EC train between there and Koln/Cologne.

Book Early And Save: Yes

Online bookings open: usually open around 6 months ahead of the travel date.

There is relatively new E.U. legislation which protects travellers against financial loss in the event of missed connections due to train delays, but it only applies to 'through tickets'.
The Eurostar terms and conditions specifically state that when booking journeys which combine Eurostar + Thalys trains 'through tickets' will be issued.
However, 'for all other journeys that combine a Eurostar Service and a service provided by another carrier(s), including when purchased in a single commercial transaction, those tickets will be separate contracts and issues regarding delays, missed connections, cancellations, compensation, and the management of aftersales will be handled accordingly'.

Though both DB, the operator of the ICE train, and Eurostar are members of The Railteam Alliance which offers a Hop on the next available train (HOTNAT) policy.
It 'allows travelers to take the next high-speed service leaving from the same station as originally planned when a delay on or cancellation of a preceding Railteam member’s high-speed service prevents them from making their originally-planned connection. This service is free of charge and is subject to the following conditions:

• HOTNAT only applies at the station at which the passenger originally planned to change trains and in cases of train delays and train cancellations.
• The approval of HOTNAT is subject to the available capacity on board each train. Seats are not guaranteed'.

So 'issues regarding missed connection and cancellations' should be 'handled' by Railteam's HOTNAT policy.
Though HOTNAT can't be applied if the arrival into Bruxelles is after the final Eurostar of the day has departed for London.

Much more info is available on this ticketing guide.

Three options to mitigate against potential complications:

1. Avoid the end-to-end journey options, which involve connecting into the final Eurostar of the day on to London:

2: Choose end-to-end journey options which have a combination of

• ICE train to Koln
• Thalys train to Bruxelles
• Eurostar to London.
  Because Eurostar does classify Thalys + Eurostar as a 'through ticket'.

3: An option is to book separate tickets for the Hamburg to Bruxelles journey with DB, and then book separate tickets for the Eurostar to London, but with an extended period of time between trains.
Then if the ICE trains on the journey to Bruxelles are cancelled or delayed, DB will issue alternative tickets to enable a later arrival into Bruxelles, as this part of the journey has AJC protection.
Similarly if the booked Eurostar train is cancelled, it will transfer tickets to a later departure.
Though if the journey to Bruxelles is so delayed that you miss the booked connection on to London, you will have to re-book the Eurostar

Seat Reservations:

The tickets will be train specific, but seat reservations are OPTIONAL on both the ICE train between Hamburg and Koln/Cologne AND the ICE train between Koln/Cologne and Bruxelles/Brussel.

The reservation fee is 2nd class = €4.90, 1st class = €5.90; but the reservation charges cover BOTH of the ICE trains on this journey.
When making a booking with DB or Trainline, you will have to add the reservations.

In contrast seat reservations are mandatory on the Thalys trains, so the ticket prices on all of the agents automatically include this reservation fee,

Reservations are also compulsory on the Eurostar and this is included when booking point2point journey tickets; your Eurostar seats will be automatically assigned.

The faster end-to-end journey:

It's also often possible to depart Hamburg 20 mins later and make an additional connection in Hannover, but because these end-to-end journeys are faster they can be the only options offered by the ticket agent.
They will be the options with 3 x transfers between trains.
If you see them SMTJ's is to avoid booking these options, they will be dependent on making a non-guaranteed connections between trains in Hannover.
Though if you make separate bookings for the Hamburg to Koln and Koln to London journeys you will have to re-book the journey on to