In danger of seeing a problem that isn't there. When you apply for your UK licence based on the EASA one, add a letter explaining that you require the FI to be included and with a brief explanation. The UK CAA will have your FI application details. If they require anything else they will ask for it.
From the recent webinars it is fair to say the CAA is keen to resolve these issues as they arise. It is likely that the website will remain behind events for some time.