Will any thickness of Kingspan K118 do for an existing wall in my house?

You do need to adjust between the different units. To work out the thickness of insulation needed for 0.30 W/m²·K you can do 0.018W/m·K / 0.30W/m²·K = 0.06m. So you will need 60mm sheet of insulation to get that target with the foam (note that this is the thickness of the foam, not the combined foam+plasterboard).

Dimensional analysis is useful for a sanity check, it doesn't make sure we have the right formula but it does help make sure we aren't wrong. W/m·K / (W/m²·K) = m which is good since we want to work out the thickness of the insulation and m is a measure of thickness.

In practice it is much more complicated because your existing walls provide some amount of insulation, how much depends on your existing wall construction, if you cavities are already insulated then this will be quite significant. So you will need less than 60mm of foam to get 0.30 W/m²·K thermal conductivity for your wall. Working this out is beyond the scope of this answer. However in the product brochure pdf on the Kooltherm K118 Insulated plasterboard webpage you linked to there are tables with estimated combined U values including a "Masonry Cavity Walls" section. So this should hopefully give you the information you need.