I'd agree with honey and lemon, I had a cold recently and have struggled to get rid of the cough as just coughing up mucus still, especially at night when it builds up while you sleep.
Steam may also help also to try and free up the mucus and trying to cough it up and out where possible, sleeping propped up a bit might help with tissues on hand to help to clear the chest where possible.
I just had to ride it out, only just mostly cleared up over a few weeks. I find this hot weather doesn't help either, though partly my asthma and hayfever there.