SN desk is not very functional on a Sunday and if you manage to talk to an english speaker it might be a Samoan or Fijian as I had a few months ago ,
I would try to go via UA tomorrow during US business hours and ask to get rebooked on different StarAlliance airline as SN from BRU to BER could be cxl depending on the priority .
SN management are talking in Belgian press about giving preference to specific flights over others ( could not find out how they put priorities on intra-Eu flights , sorry ! ) as this is start of Easter vacation for flemish speakers which are going nuts over getting their schoolvacation cancelled ...
Easter vacation is also moment when many schools in Flemish Belgium go on 1 week schooltrips abroad so you might be lucky if your flight has an entire class of kids and teachers going to visit BER !

There are flights open from LHR to BER with LOT ( leaving around 6 pm for 236 pounds) , OS , LH( leaving around 6:30 pm ) and LX just looking at members of Star-Alliance group .
If SN does cancel your flight or lets you rebook via UA there is ample choice and they should rebook you for free as this is not 'an act of God' so they pick up the tab. Talking on the phone with a smile will get you a lot more help than getting smart with an already overworked and underpaid call center !!