How to get a fixed amount late charge / penalty on an invoice irrespective of its overdue amount ?

Summary:
I have a business requirement to apply a fixed amount penalty as late charge if an invoice is overdue even after 28 days of its original due date.
For Example:
Invoice Date: 1st Apr
Payment Term: 30 Net
Invoice Due Date: 30 Apr
Grace period: 28 Days
Late Charge/Penalty: £10 if not paid by 28th May (incl. grace period)

I have created the receivable activity with type as Late Charges; I have enabled the "Assess Late Charges" flag and assigned the receivables activity to Penalty option in "Manage Receivables System Options"; I have created the customer profile class with only late charge (Penalty) fields leaving interest related fields blank. And still when I run "Create Late Payment Charges", in-spite of eligible transactions, no adjustment gets applied to the invoice.