How can I make a series of actors follow one another precisely

Look at the physics constraint actor, linking a few of them together could get your desired movement.

I know this is a rope but when lying on the ground and being dragged from the front it should look alright.

https://docs.unrealengine.com/latest/INT/Engine/Physics/Constraints/ConstraintsUserGuide/index.html

There is a also demonstrations of its use in the content examples in the physics bit