Earl, I would have thought that you would need an Icelandic validation to fly to their FTL scheme or rules. Assuming you are employed on a UK contract, without such a validation then you are beholden to English law and CAP 371 only.
Have you asked your Company about this?
After all, if you have an accident or incident on a TF registered aircraft when operating outside CAP 371 can you be prosecuted in the UK?
Equally, would the company's insurance poilicy be valid if it could be proved you operated illegally?
Proceed carefully.