The Daily Mail article doesn't specify the exact source of the quotes it's using, but I'm pretty sure their source is the Human Rights Watch World Report 2013 on Turkmenistan:
Following February 2012 presidential elections, President Gurbanguly Berdymukhamedov retained unchallenged power, and Turkmenistan remains one of the world’s most repressive countries.
The country is virtually closed to independent scrutiny, media and religious freedoms are subject to draconian restrictions, and human rights defenders and other activists face the constant threat of government reprisal. The government continues to use imprisonment as a tool for political retaliation.
Turkmenistan continued to expand relations with foreign governments and international organizations in 2012, but without meaningful outcomes for human rights.
The report is fairly long and fully available online, I don't think it would make much sense to copy it here. Other than this report, the HRW maintains a page about Human Rights in Turkmenistan with various other reports and news articles about human rights violations.
Moving on, the Office of the United Nations High Commissioner for Human Rights (OHCHR) has published various reports on Turkmenistan since 2006 (when Mr. Berdimuhamedow came to power), all with long lists of "areas of concern and recommendations":
Again, those reports are fairly long and can't be easily summarized here, but even a cursory reading indicates that the UN, although a lot more diplomatic in its verbiage, doesn't disagree with the HRW about the status of human rights in Turkmenistan.