Can only reply about two specific types...B707 and L1011.
For both (using round numbers), it requires approximately 500kg/hr more to cruise with one engine shutdown.
Sometime in the early seventies, DanAir, who at the time were operating the Comet4, asked the ARB if it would be OK to shutdown one engine in cruise...as on this specific type (according to them) fuel savings could be had.
DanAir was politely told....no. This was reported by Flight International at the time.
Others, who indeed have operated the Comet (or the Nimrod) may have additional comments.