Authorities in Iceland have told a couple they will not renew their 10-year-old daughter’s passport on the grounds that she is called Harriet – which is not on a government approved list of names.

British-born Tristan Cardew and his Icelandic wife Kristin are appealing against the Reykjavik National Registry’s decision, which also does not recognise the name of Harriet’s 12-year-old brother Duncan either.

"The whole situation," Mr Cardew told The Guardian, "is really rather silly.”

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Both children have been travelling on passports identifying them as Stúlka and Drengur Cardew, or girl and boy Cardew. But now authorities are refusing to issue new passports due to law that states no official document can be given to people who do not have an approved Icelandic name.

The Cardew’s were forced to apply to the British Embassy for an emergency UK passport in order to travel to France for a holiday next week, the newspaper reports.

The law directs that unless both parents are foreign, the names of children born in Iceland must be submitted to the Registry within six months of their birth. If their name is not featured on a list of 1,853 female and 1,712 male approved names, parents are required to seek approval from the Icelandic Naming Committee.

The committee reportedly receives about 100 applications for the average 5,000 births each year, and in 2009 rejected 46 out of the 105 which were submitted for approval.

According to the Reykjavik Grapevine, the law states that “forenames shall be capable of having Icelandic genitive endings or shall have become established by tradition in the Icelandic language,” and “names may not conflict with the linguistic structure of Icelandic”.

This means that names containing letters such as ‘c’, which does not officially exist in Iceland’s alphabet, are off the table as far as the law is concerned. Harriet's name was rejected on the basis that it cannot be conjugated in Icelandic, Mr Cardew said.

The couple could solve the issue by giving Harriet an Icelandic middle name, but rejected such a move as “silly”. Mr Cardew, who has been living in Iceland for 14 years, added: "Are they saying they don't want us here?"

The law also has a clause prohibiting parents choosing first names that could cause their children embarrassment, stating: “A forename may not be such as to cause its bearer embarrassment.”

It has come under increasing scrutiny over the past few years, and was even lambasted as an "unfair, stupid law against creativity" by Reykjavík mayor Jón Gnarr on his Facebook page.