If you are a Hilton whore, and there are plenty here, then the obvious thing to do is to take a NCL flight the night before, stay at the Doubletree either on the very cheap overnight cash reservations that they offer, or on points/points+cash, it's normally in one of the lowest bands and yet it's one of the better Doubletrees. Then take the 06:05 flight from there to LHR. It overnights at NCL and because of crewing needs, it is a reliable service, if somewhat anti-social and gets you airside without further security for 07:20. Almost worth it to avoid T5 security, some would argue!

The Doubletree is almost by the domestic arrival door at NCL.

Personally I wouldn't advise the Manchester service, too risky, ditto any back to back at that hour.