Ewa here from the Engineering Team at FreeAgent — thanks for your message on our forum.
I can see you’ve spoken to our Support Team regarding this question — I’m afraid in this instance, the API doesn’t offer any additional workarounds compared the the web app. The suggested solution to create an invoice with two line items (one with the unit price of £8.32 and then another line item for 1p), although I understand is not quite what you’re looking for, can also be implemented via the API by passing an array of line items when creating an invoice.
Alternatively, you can decide to generate your invoices outside FreeAgent but still account for them by explaining income to Sales.
As promised, my colleague from the Support Team you spoke to has recorded the ability to calculate VAT in reverse from gross totals as a feature request in our internal system, so it will certainly be reviewed by our Product Team.