Generally, I wish to plot a rather complex x-y plot (lots of overlapping curves) to an A3 format so: 

A4 210x297  
A3 = A4*2 = 420 x 297  
... - 10mm each side = 400 x 277 (size of desired plot window)

What is the easiest way to set the size of the plot so it fits that size when printed in PDF (or any other common output format)? 

As @LewisNorton explained, you need to set the Paper*** properties of the figure. Below is an example for producing a PDF file with dimensions 420 x 297 mm (A3 size), where the margins between the plot and the file borders are 10 mm each (top,bottom,left,right). 

%# centimeters units
X = 42.0;                  %# A3 paper size
Y = 29.7;                  %# A3 paper size
xMargin = 1;               %# left/right margins from page borders
yMargin = 1;               %# bottom/top margins from page borders
xSize = X - 2*xMargin;     %# figure size on paper (widht & hieght)
ySize = Y - 2*yMargin;     %# figure size on paper (widht & hieght)

%# create figure/axis
hFig = figure('Menubar','none');
plot([0 1 nan 0 1], [0 1 nan 1 0]), axis tight
set(gca, 'XTickLabel',[], 'YTickLabel',[], ...
    'Units','normalized', 'Position',[0 0 1 1])

%# figure size displayed on screen (50% scaled, but same aspect ratio)
set(hFig, 'Units','centimeters', 'Position',[0 0 xSize ySize]/2)
movegui(hFig, 'center')

%# figure size printed on paper
set(hFig, 'PaperUnits','centimeters')
set(hFig, 'PaperSize',[X Y])
set(hFig, 'PaperPosition',[xMargin yMargin xSize ySize])
set(hFig, 'PaperOrientation','portrait')

%# export to PDF and open file
print -dpdf -r0 out.pdf
winopen out.pdf

Without a printer at hand, I am using a virtual screen ruler to check the measurements; Simply display the PDF file with your preferred viewer, and the set the zoom level at 100% (I am using Sumatra PDF). If you want to try this yourself, just be aware that some viewers (Adobe Reader) might be using a custom DPI not matching the system default resolution (mine at 96 pixels/inch).

Here you can see the bottom and left margins equal to 10mm. The same holds for the other two margins: 

Note that in the example above, I made the axis cover the entire figure (no gray area in the figure). By default, MATLAB leaves some empty space for tick labels, axis labels, title, etc.. This is of course different from the margins mentioned above, which I assume you already know :)