Thanks everyone for your help. The answer I am now using (courtesy of
Mrexcel.com) is very elegant and works in all circumstances I have
tried. Thought you might be interested in it too:

=IF(OR(AND(startHH=1,startHH<4), AND(finishHH=1,finishHH<=4),
AND(finishHH=4,finishHH-totalhours<4)),"Yes","")

This works for finish hours in 24 hour format but it was quite simple
to adjust to suit my spreadsheet. It returns "Yes" if any hours were
worked between 1am and 4 am and I have been able to take it from
there.

Buggered if I know how it works but it does!