I don't know but the other service that was operated by Eastern from LCY (to IOM) was taken off Eastern and given to Loganair after a string of last minute cancellations. I suspect BACF's patience with Eastern is wearing fairly thin.
If you want to be rebooked on alternative airlines then you need to go to the airport to do it. The contact centres and BA.com don't offer that service, but airport staff can do it. You should be able to claim a refund on the ticket plus either 0€, 125€ or 250€ depending on the exact timings offered to you by BA or BA.com.
EDIT: The dispatch information says it's crew related (as in not enough of them), and the Y means yes to EC261. The time of cancellation was 11:14 CET.
DOBA3276/16SEP
* OPERATIONAL FLIGHT INFO * BA3276 0 SU 16SEP18
CITY INFO HOUR (LOCAL)
DUS ESTIMATED TIME OF DEPARTURE 1800
FLIGHT CANCELLED 0414
CCRY
ESTIMATED TIME OF ARRIVAL 1815 LCY
*1A PLANNED FLIGHT INFO* BA3276 0 SU 16SEP18
APT ARR DY DEP DY CLASS/MEAL EQP GRND EFT TTL
DUS 1800 SU JCDRI/M YB/S E70 1:15
HKMLVNOQSG/S
LCY 1815 SU 1:15
COMMENTS-
1.DUS LCY - AIRCRAFT OWNER EASTERN AIRWAYS
2.DUS LCY - OPERATED BY EASTERN AIRWAYS FOR BA CITYFLYER
3.DUS LCY - 9/ NON-SMOKING
4.DUS LCY - ET/ ELECTRONIC TKT CANDIDATE
5.DUS LCY - CO2/PAX* 63.48 KG ECO, 63.48 KG PRE
(*):SOURCE:ICAO CARBON EMISSIONS CALCULATOR
CONFIGURATION-
E70 C 8 M 68