Hackers say they have posted details of a 'have an affair' site users online, with as many as one million UK love cheats reported to be among the names.

Website Ashley Madison, which has the tagline "Life is short. Have an affair", was hacked last month by a group calling itself The Impact Team.

The hackers, who said they had complete access to a database of more than 37 million members, now claim to have fulfilled their threat to post customer records online.

The hack is understood to be a protest over the charging of a leavers' fee to users to completely delete all their data.

The Impact Team said the erasing of personal information is a "complete lie", and claimed that details such as real name and address are never deleted - information the hackers suggest is likely to be "the most important" that users want removed.

Avid Life Media (ALM), which runs Ashley Madison as well as dating sites Cougar Life and Established Men, said it is investigating the latest claims "to determine the validity of any information posted online".

In a statement ALM said: "Furthermore, we will continue to put forth substantial efforts into removing any information unlawfully released to the public, as well as continuing to operate our business."

The information has reportedly been posted on the Dark Web, which cannot be accessed with the usual search engines such as Google, instead requiring the use of a covert internet browser called TOR.

The Dark Web is described as the "underground of the internet" or the "internet black market".

ALM said it would work to ensure those behind the attack will be held to account.

"This event is not an act of hacktivism, it is an act of criminality. It is an illegal action against the individual members of AshleyMadison.com, as well as any freethinking people who choose to engage in fully lawful online activities," said ALM.

"The criminal, or criminals, involved in this act have appointed themselves as the moral judge, juror, and executioner, seeing fit to impose a personal notion of virtue on all of society.

"We will not sit idly by and allow these thieves to force their personal ideology on citizens around the world. We are continuing to fully co-operate with law enforcement to seek to hold the guilty parties accountable to the strictest measures of the law."

ALM appealed for anyone with information on the hack to come forward.

In a 2012 study by online rights campaign group EFF, Ashley Madison was praised for the way it deleted data after a user closed their account.