W6 2371 then FR 2082 at Madrid
Budapest → Madrid → Birmingham (UK)
Timetable, Madrid time
19:15W6 2371 from Budapest at the gate
10:05FR 2082 to Birmingham (UK) leaves the gate
14 h 50 apart on the timetable, overnight
FR 2082 leaves 14 h 50 after W6 2371 arrives on the timetable: more than half a day, so not a connection we count.