The billing is the invoice.
Several ways to go forward, but probably best to ring them, state the obvious and ask why they have not paid you. Best to do this over the phone as you can gauge the extent to which extracting the money is going to be a problem. It also enables you to check that they are happy with the work (ask them).
Try and avoid the cheque in the post promises - offer to go and collect the cheque.
If you are not getting anywhere, the end-point is a threat, then action, to take them to the small claims procedure in the County County to try and recover your money. Doesn't cost much to invoke, and if successful, gets a court order for you to be paid.