Ifonly is correct....the question is 'free circulation' not 'VAT paid'. This meets the criteria for free circulation.
There is no such thing as a 'certificate' of free circulation....the HMRC specialists used to examine the docs and write a letter. That no longer happens.
A C88 is the best proof of import.....it is a common format to all EU countries and recognised by all inspectors. I don't understand why you couldn't have got one of those on import; it is not dependant on actual cash being paid. Have you contacted your shipper and asked if the C88 was issued for this aircraft? Shippers are simple souls and probably don't realise the significance of such a document to an aviator.