Firstly, your ex owes *you* the costs of the divorce. *You* owe your solicitor for the costs incurred. The liability never passed from you to your ex - you issued instructions and incurred the costs therefore you have to discharge them.
If an order for costs is made that said something along the lines of "to be assessed if not agreed" this means that the costs have yet to be quantified. You will need to serve a bill of costs upon your ex which details the costs incurred within the divorce suit. This is something that your solicitor should do.
If the order specifies a sum e.g. "the response do pay the sum of £1000" this can be enforced against your ex which is relatively simple but involves a civil claim which is cheap and easy. It is important to note that you cannot get blood out of a stone so if your ex lives in a cardboard box at the back of Sainsburys you will be on a hiding to nothing.