Bomb loads and fuel loads are not a constant. An unladen Lancaster could fly with little problem on two engines, if a pilot lost one engine approaching the target he was definitely safer continuing to the target as compared with flying across or against the bomber stream. However a Manchester with engines de rated to 1450 BHP had less power than a late war Lancaster on one engine, though the Lanc was heavier with more drag. But mainly, losing an engine on a Manchester happened often with no enemy action needed.I'm not sure that either a Lancaster or B-17 could fly on one engine when fully loaded with bombs and fuel.
Most of the stories of those flying on one engine are returning to base, low on fuel and bombs (and some part of their ammo).
If a 4 engine bomber lost two or more of its engines on the way to the target the crew would most likely jettison the bombs and turn for home.