In response to the comment above, the relevant section of makePlot[] looks like this:

result = ListLinePlot[.....]
Return[result]

and makePlot[] is called in this section of code (aciid1 and acid2 are the source data for the PopupMenus)

Style[Dynamic[$Version], DynamicUpdating -> True];
(*Dynamic[myPlot]*)
myPlot = makePlot[];
Grid[{{"First acid", PopupMenu[Dynamic[acid1], menuData], 
   ""}, {"Second acid", PopupMenu[Dynamic[acid2], menuData], 
   Button["Display", myPlot = makePlot[]]}, {"", Dynamic[myPlot], ""}}]
(*Dynamic[myPlot]*)

I have used Dynamic[myPlot] in the third row of the grid, but the two commented lines show that it could also be used before or after the code which creates the PopupMenus and Button.

myPlot = makePlot[] is called for the initial display and then called each time the button is clicked

If asked, I can attach the entire notebook.

I was not all hopeful that I was thinking along the right lines, hence my question, but as it turns out this was far simpler than I anticipated. It's working like a charm.

Still, somebody might find this useful (I have seen other posts about clearing output ...)

I'd be happy to provide more detail if anybody is interested.