This depends on the cause of your chesty cough of which there are many. I assume that you are generally healthy and do not suffer from one of the chest or lung illnesses such as chronic bronchitis which can give you a chesty cough.
If so, the most likely cause of your chesty cough would be a viral or bacterial infection of the upper airways, the most common of which is of course, the common cold. If the initial cold symptoms have resolved, you should find help from the herbs ivy and thyme (as found in Bronchoforce). It may also be of benefit for you to reduce the amount diary produce (eg. milk, cheese and yoghurts) you consume until the problem goes away as these are thought by naturopaths to be ‘mucus producing’ foods.