I can't seem to create an arc of (say) 65 degrees with a diameter of
50mm - I never see entry boxes with 'width', 'height', 'start' and 'end'
displayed at the same time for me to fill in precise values.

Jim here's what I'd do.

Set up some guide lines so you have a 50 mm "box".
Select the ellipse tool and draw a circle by holding down control and dragging from corner to corner.
Enter the start angle where you like it. (Inkscape denotes the 3 o'clock position as 0° and proceeds to 360° in a clockwise fasion.)
Enter an end point equal to the start point plus the desired arc lenght, in this case 65°.

I hope that's fairly straight forward.

Aaron