I think you miss labelled your boarding and bag drop times (21:40, 21 20). With a 1:50 connection time it is doable but very very tight considering you'd have to deboard the your flight from HKG (I assume you mean Hong Kong (HKG) and likely on to/from Shanghai (PVG) with cathay dragon?), collect your bag and go airside before switching terminal in ~ 1 hour. Are you business or first on your flight from HKG and may your checked luggage be prioritised during unloading plus deboard early? Without that I'd say your only chance is hand luggage only and you'll probably still be moving swiftly given how frequent slot delays are at heathrow but you could definitely make it. It's also the last flight out to DUB so unfortunately your risking staying the night.
I would have thought that as BA codeshare EI's flights that you would have been able to get that all on one booking through cathay and BA oneworld connection, guess not.