What does an invoice actually do?
An invoice is the formal ask for money. A quote says what a job will cost; an invoice says the job is done, or a stage of it is, and here is what you owe and by when. It is also the record both sides keep — the customer files it as a purchase, you file it as a sale.
In the books it does two things at once. It records the sale as income on the date it was raised, whether or not the money has arrived, and it creates a debtor: an amount the customer now owes you. When they pay, the debtor clears and the bank balance rises.
If you are VAT registered the invoice is also a tax document. HMRC requires certain details on it, and the customer needs it to reclaim the VAT you charged, so a sloppy invoice can cost them money and make them slow to pay you.