Aucklanders who fancy popping down to the library to read some of their favourite British tabloids online could be out of luck.

The Daily Mail and Daily Star websites couldn't be accessed by the computers available for public use at Auckland's Central City library on Thursday.

But other tabloid sites, including The Sun, The Daily Express, The Mirror and the New York Post, were accessible.

Auckland Council's digital and service development manager Greg Morgan said there was no specific list of blocked sites maintained by the council.

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Instead, access to websites was only restricted when certain kinds of content were detected by filtering software.

This included "adult content, harmful and stealth content, and hacking content," Morgan said.

If library users thought blocked websites were not objectionable, library staff could provide manual exceptions.

Hamilton's public library internet users are banned from looking at websites containing porn, torture, cruelty, violence or bullying or anything that promotes exploitation of children for sexual purposes.

Access to sites that promote criminal acts or terrorism, or those which represent any class of society as being inferior to others is also prohibited.

The policy is similar in Tauranga, where kids younger than 16 need a signed consent form from a parent or caregiver to access the net.

In Wellington, the right is reserved to deny access to people misusing library internet services through cyber bullying and harassment, illegal downloading or accessing porn and other objectionable material and Christchurch and Dunedin libraries use filtering software as in Auckland.

The inability to access some tabloid media sites is on the flipside of the library's stance last year against the pulling of Ted Dawe's controversial teen novel Into the River from shelves around New Zealand.

Also in 2015, the council was criticised for a flaw which allowed its Wi-Fi users to access pornographic images through Google image searches.