Overnight? Wow.. Well if you look at a map Rome is pretty far south. If you insisted on going this route you would be a bit grubby on arrival.
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London Waterloo Int. dep 09:09 EST 9012 EUROSTAR
Subject to compulsory reservation, Special ticket or supplement required, Please observe check-in times, Non-smoker train, Bistro Cafe
Paris-Nord Eurostar arr 12:53
Paris-Nord Eurostar dep 12:53 transfer 80 min.
Paris Lyon arr 14:13
Paris Lyon dep 14:24 TGV 9247
EC 9247 TGV
Subject to compulsory reservation, Global price, Bar coach, space for wheelchairs
Runs as TGV 9247 up to Oulx-Cesana-Claviere, then as EC 9247
Torino Porta Susa arr 19:46
Torino Porta Susa dep 20:43 IC 624 InterCity
space for wheelchairs
Torino Porta Nuova arr 20:55
Torino Porta Nuova dep 21:45 D 1665 Schnellzug
Roma Ostiense 19.12.04 arr 04:37
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So 9AM to 4AM the next day.. well it would be overnight once you reached Torino, IT.