Hi Piers,
on the record type that the email is sent from you need to add a text formula field that pulls in the HTML.
You may need to add a step that saves the form (creating the connection to the record with the HTML and pulling it through) and then a second action that issues the email. This could be done with an auto-submitted form. There’s a bit in here about auto-submitting forms; let me know if that isn’t clear.
Hope that helps!