The first thing to note is that, in my experience, Eurostar are great when it comes to putting you on the next available service if DB has caused you to be late - even if you turn up the next morning/midday because delays meant you had to have an overnight stop in Cologne or Brussels.
As regards reliability of Berlin to Cologne and Cologne to Brussels: I used to do this trip regularly, and I think I only once didn't have a delay between Berlin and Cologne, although it was usually less than 20 minutes and just meant added stress making the connection at Cologne (ie running between platforms).
Since DB's ICE to Brussels is usually scheduled to arrive at least 90mins before Eurostar departure, you already have a built in buffer there, and Eurostar are great at rushing late passengers through security etc to get them on board (have been delayed for a few minutes on a Eurostar in Brussels a few times to allow late boarders). So usually this leg is stress free, at least as far as making the connection goes.
If you're going further than London, it's definitely worth considering an overnight in Cologne or Brussels. It makes the trip a lot more relaxed (unless you enjoy sitting on trains all day long, of course, which many here seem to), and both are great cities to spend a pleasant evening in. You can add a stopover in Cologne (or anywhere else) in your Berlin-Brussels ticket, but it's also worth comparing prices with two tickets (B-K, K-Brussels).
Finally, DB International now has a small contingent of 'through' tickets to London which aren't actually through tickets, but two different tickets. Doesn't look like it's worth going down this route (see
https://jonworth.eu/how-to-use-deut...s-for-train-trips-between-germany-and-london/) and I just get the DB and the Eurostar tickets separately nowadays.
PS As ever, the Man in Seat 61 does an excellent guide to this kind of journey:
https://www.seat61.com/Germany.htm#london-to-berlin-by-train