This is a tricky one. As I see it, there's a bit of a difference between what the customer wanted, and what the customer got.
At the moment he has an unsatisfactory EICR which is no use to him for letting the house, i.e it does NOT say the wiring is safe.
What he wanted was a satisfactory EICR.
Now the problem is, you want payment for the EICR, then you will do the remedial work and ask for payment for that.
On the other hand, I'm willing to bet the customer is waiting for the quote, and if it's reasonable, will ask you to do the remedial work and then pay for the whole lot together.
The key thing here is to communicate with your customer so you both understand each other.
This also highlights why, where I can, I will do "simple" remedials at the time of the EICR so it's all done and dusted in one visit. e.g I would have at least tried to identify and fix the broken ring neutral rather than just leave it.
As for genuine non payers, I usually find (after giving them a reasonable time to pay) a letter stating if it's not paid in 14 days, you will hand it over to a debt collection agency usually does the trick.
Also, your invoice should state terms and conditions. Mine say payment must be made within 30 days, otherwise I will charge interest a 4% above the BOE base rate until payment is received.