What ratio of honey, lemon and hot water is used to make the cough medicine. Also I tried it with ginger, not only was it horrible it was very gritty, maybe used too much.
You could try it in a herbal tea, I have camomile tea (currently a Camomile and Spiced Apple or Camomile and Honey ones) and squeeze some honey onto the bottom of the cup and a slice of lemon, leave it a little bit so that the tea bag infuses the water and honey. There may be some teas with ginger in too. Twinings do lots of different sorts.
I'm not a big fan of honey on its own but don't mind if it's in some as long as the taste isn't strong. Rowse do a mild version.
I haven't used it for a cough but might help you with the taste.
If you used ground ginger, the stuff you use in cakes, no wonder it was gritty. You should use crushed ginger root, tied up in a bag and boiled, then with extra ingredients added for flavour and sweetening.