FR 338 then FR 670 at Dublin
London Luton → Dublin → Birmingham (UK)
Timetable, Dublin time
20:55FR 338 from London Luton at the gate
13:20FR 670 to Birmingham (UK) leaves the gate
16 h 25 apart on the timetable, overnight
FR 670 leaves 16 h 25 after FR 338 arrives on the timetable: more than half a day, so not a connection we count.