You sound as though you are describing a broken tensioner.
The only tensioner movement I would expect is that from left to right, not up and down, as you have described. The tensioner will only move when the engine rpm changes rapidly.
Take a look at Help Anybody know how to manipulate the chain and chain tensioner on a V12 HE and read the whole thread to decide whether your timing chain is worn down too much.
See also http://forum.etypeuk.com/viewtopic.php?f=6&t=12004&start=28 which shows a broken tensioner which will skip up and down as you describe and also make a rattling noise if the engine is running.
kind regards
Marek