There's a bit of a divide between the American and UK/Aussie schools of helicopter aerodynamics teaching, from what I've seen.
Simplistically speaking:
The yanks (or some, at least) favour the use of gyroscopic precession to explain why a control input has its effect 90 degrees later in the rotor blades' direction of rotation - ie a force applied to a spinning gyro will cause a tilt 90 deg. later.
Thus, for a forward cyclic input on a helicopter in the hover, the pitch angle on the blade is at a minumum directly out to the right hand side (for a US-direction of rotation blade), but the disc will be lowest at the front. Explanation - gyroscopic precession.
The poms say, though, imagine that same cyclic input, where the pitch is lowest out to the right.
Say the disc started out level, in the hover. A forward cyclic input will reduce the pitch on the blade on the right hand side of the disc in this fashion, considering the blade sweeping around from back to front:
Just slightly round from the back, there'll be a small pitch reduction, getting bigger so pitch angle is lowest when the blade's directly out to the right, then coming back from that low setting until it's back to neutral at the front (and will then get relatively bigger in a similar way on the left hand side).
However, the key point is that whenever the pitch is lower than the original disc-level hover setting, the blade will be flapping down, slowly at first, reaching a maximum rate out to the right, and reducing to nearly zero approaching the front - which is where the blade reaches its lowest point and starts going up again, of course.
This explanation is my favoured one because it makes aerodynamic sense to me. Blades on a rotor head aren't the same as a gyro because they're not rigidly in plane all the time, but flap up and down (and lead and lag) to the extent of the flexibility of the materials and the hinges.
They are big and heavy though, and spin bloody fast, so I'm not saying gyroscopic forces don't exist, just that I find the aerodynamic explanation of how they move to be more compelling and believable.
Flapback:
Disc starts out level, increasing airspeed causes lift increase on advancing blade, maximum at position directly out to the right, vice versa on retreating blade.
Point of max lift increase is where blade will be flapping up fastest, progressively reducing around the advancing side until we reach the front of the disc, where it has reached its maximum amplitude of flapping up and starts to go down again.
Inflow roll:
As helicopter moves forward, air at rear of disc has spent more time over it and has relatively higher downward velocity than that at the front.
Therefore there is a greater lift reduction at the rear of the disc due to this greater inflow, so the disc should be flapping down at the highest rate at the rear, continuing to do so until it reaches its lowest point half-way round on the advancing side. This results in a roll towards the advancing side.
NB: Disclaimer ... all off the top of my head, having not thought about it for a good few years, so I'm not saying this is all kosher!