About UK Milliradians
The UK milliradian is one thousandth of a radian, or 0.0573°, so 6,283 of them fit in a circle. At 1 meter it spans 1mm.
An object that fills 1 milliradian of your view is 1 meter wide at 1km, or 1mm wide at 1 meter. Divide the width by the angle to get the range – a 1.8m person covering 3 milliradians is 600m away.
Degrees don't give you that shortcut: at 1km one degree is about 17.45m wide, which is nobody's idea of a round number.
About NATO milliradians
One NATO mil is 1/6,400th of a circle, or 0.05625°, so a degree is about 17.78 NATO mils.
A NATO mil is close enough to a true milliradian (6,283 of those make a circle) that gunners treat it as 1 meter of width at 1,000 meters of range. A circle of 6,400 also divides neatly into quarters, eighths and sixteenths.