Thanks for all your input guys.
firstly, there is a contract in place, stating that stuff out of scope is billable. Unfortunately, at no point did we put a timeline to it, as they didn't know when they would be ready to launch.

Also, fortunately, at each interval where a new set of whatever was requested, I sent them a quotation which was signed off. So in that respect, they definitely know that they are incurring extra costs

I will not be handing any deliverables over until the payment is settled in full.
I have sent them an invoice for the additionals that were completed. Until now, they have not made the payment. So I presume that they will be paying the whole lot at once. But I reiterate - their site will not go live until such a time that all monies have been paid in full.