BA 553 then EI 169 at Heathrow
Rome → London → Dublin
Timetable, London time
16:35BA 553 from Rome at the gate
16:20EI 169 to Dublin leaves the gate
23 h 45 apart on the timetable, overnight
EI 169 leaves 23 h 45 after BA 553 arrives on the timetable: more than half a day, so not a connection we count.