Assuming (looking at one sise of the staircase):

|
|--- wall
|
|a
|#
|# ---- string of staircase
|#
|#
|#
|#
|b
|
|
|

We are talking about gaps visible between the wall and the string that
you can see at "a" and "b", then I would expect that the string is
painted / varnished / finished etc as the other woodwork in the
locality. In which case just fill the gap and finish to math the wood
rather than plastering anything.



Yes that sounds about right - but also in the room beneath the stairs
you have (side view of the wall)

|- - ---x
| |
| |
|- - --y
|
|
|
|
|
|_ _ floor__

It's at x and y that the plaster has cracked - so I can fill it, fine,
but I was thinking that if I perhaps add more plasterboard and plaster
over that, it will conceal the movement (and any sub sequent cracks)
better.

I may be being naive there...