HMRC expects every invoice you issue to carry a unique number, and if you are VAT registered the numbers must run in sequence: 1001, 1002, 1003, with no gaps you cannot explain. A gap is not an offence in itself, but you should be able to say what happened to the missing number - a cancelled invoice, a voided draft - because an inspector will ask.
Any format works as long as it is unique and sequential: a plain count (INV-1001), a year prefix (2026-001), or a prefix per customer (ACME-014) if you run one sequence per client. Never reuse a number, and never renumber an invoice you have already sent; issue a credit note and a new invoice instead.
In FullDiary the invoice number box sits at the top of the form, next to the issue date. A new business starts at 1001 - nobody needs to know they are your customer number one - and every invoice after that takes the next number automatically. Quotes have their own sequence starting at QUO-1001.
Type a different number in the box if your accounts already run a sequence; FullDiary carries on from whatever you set. Clear the box and no number prints on the invoice, the PDF or the online copy.
You can also just tell the AI creator: "make this invoice 2050" or "remove the invoice number".