We have a (standard double) wooden base with slats six inches wide with one and a half inch gaps between them. There is also a centre rail with a leg to support the slats so essentially they are rigid.
We want a new pocket sprung mattress, do I need to cover the slats with plywood or some type of cushioning?
With the base as you described I would definitely look at putting some mdf/ply down on your slatted base. There is a considerable difference in user comfort levels between a mattress on a sprung edged divan base, and a mattress on a sprung (or solid) slatted base. Pocket springs work best when there is a system of gradual suspension. This means that as the weight applied to the mattress is under duress, the springs in the mattress takes the strain and the springs in the base cushions the blow if you will.