I have answers to your questions and a workaround for the Tax Reg. No not showing in the Customer Details section, @daveyj1.
The Tax Registration Number is not displayed in the Customer Details works as intended in QuickBooks Online. As a workaround, you can add it in the Notes section.

No worries because the Tax Registration Number will display in the invoice form. See the sample screenshot below for more reference:

I agree with SME Bookkeeper that it's essential to accurately record your VAT to submit correct tax forms and payments to the HMRC. For more information on handling your VAT, check out the following articles below:
Additionally, read the following links below to know the different VAT codes and how to use these in QuickBooks:
I am delighted to have been able to help you today. Please don't hesitate to mention my name if you need further assistance. Keep safe.