Why doesn't a recorded VAT payment match itself to my bank record for an identical amount on the same date? The bank register is now showing two payments.

Thanks for visiting the Community, @BruceL. Based on your statement, the other payment is posted as a journal. If you've recorded your VAT payment through a journal entry, this can be the reason why it shows duplicate records in the bank registers. 

To fix the issue, you're in the right direction to exclude the duplicated one. Here's how: 

1. Go to the Banking menu.
2. On the Banking page, click the For Review tab.
3. Check boxes of the transactions to exclude.
4. From the Batch actions drop-down, choose Exclude Selected.

For future reference, instead of recording your VAT payment using the journal entry, I'd suggest you record them on the Taxes page to avoid duplicates. Then, match them to the transactions on the Banking page. 

Here's a great source of information that you can follow: How to record a VAT payment or refund. It also includes a short video clip that can guide you through recording VAT payment in QuickBooks. 

Feel free to message again if you have additional questions. We're always delighted to assist.