Correcting VAT Claimed on previous return

is it acceptable on next return to issue refund of the vat via a credit note on the original purchase like this

Net 0.00
VAT -6.25
Total -6.25

This then adds it to the next vat return as due to hmrc ?

Also, the amount refund in vat, it has been paid, just not vat, so would i re-issue an invoice to the supplier with no vat for the above amount, assuming that a VAT credit note is acceptable, as long as records are kept about the mistake.

Only reason i ask is i submitted a vat return with a few invoices from one supplier whos site sated that all prices included vat at the time i was doing the paper work, but the supplier apparently wasnt vat registered at the time i was supplied, so my assumption was wrong while i waited for copies of the invoices, i now have these but however they are VAT free due to them registering for VAT at a later date than my invoices.

The above is taken from this on another well know site

Purchase invoice > Paid > VAT Cash Accounting > Entered in error or you need to amend it > Included on a VAT Return
You can’t delete a payment once you’ve included it on a return.
Instead, to cancel the values of the payment, you need to record a
negative payment against the invoice. The invoice then becomes
outstanding and the next time you create your return, the negative
payment is included and corrects your liability to HMRC.

However their system works different to this one