CAP 493 (The UK Manual of Air Traffic Services Part 1) states that the word 'degrees' should be appended to heading figures where the heading ends in zero, or in cases where confusion or ambiguity may result.
So, "Heading 320 degrees" is correct for an ATC instruction, but I'm not aware of any specific requirement that mandates the word 'degrees' in the read-back, but I guess the same principle applies.