If this fails to get a satisfactory response, it may help to involve more senior people in the customer organisation. For example, you could send copies of your correspondence to the finance director; depending on the circumstances, the finance director might then instruct his subordinates to make payment. Likewise, if you were having difficulty getting payment from a school, you could contact the Chair of the Board of Governors. Sometimes, a friendly high level approach (from, say, your managing director to the customer's managing director) can yield results.
If the dispute is with a customer with whom you expect to do more business, the wording of your correspondence can have a significant impact. Provided that you are being reasonable and professional, a dispute and even a legal case need not necessarily mean the end of the business relationship. It may be worth emphasising that you have supplied the products (or services) for which you seek payment, and that you still wish to maintain the friendly and mutually beneficial relationship that you have enjoyed up to that point.
But remember, the chances of recovering a debt decrease with each day that passes. If you are unable to recover the debt within a reasonable timeframe, you may need to consider contacting a solicitor (or debt collection agency).