The council said it had reduced the number of sunbeds at its centres from seven since 2008.
The report said the risk appeared to be particularly high when using sunbeds at a young age.
Under new laws proposed by the assembly government, children would be banned from using sunbeds in Wales.
Many children and teenagers appeared to be using sunbeds without supervision, with 23% using them at home.
The council has two sunbeds at Penarth Leisure Centre and one each at Barry, Llantwit Major and Cowbridge.
The committee decided to hold an inquiry following a number of reports of children being burned whilst using sunbeds.
Dr Andrew Dearden, from the British Medical Association, told AMs that sunbeds were dangerous and should be regulated more effectively.
She added the best way to prevent melanoma was to avoid damage caused by too much sun exposure and sunbeds.
According to the BMA, it is one of only two councils in Wales that allow sunbeds to be operated in its leisure centres.
They found the cancer risk from sunbeds was more than twice that of spending the same length of time in the midday sunshine.
Justine Sheils, a 37-year-old administrator from Liverpool, began using sunbeds when she was 15 and was diagnosed with malignant melanoma five years ago.
The singer said a recent trip to her home city of Liverpool left her shocked after she realised how many young girls were using sunbeds.
Ms Harris called for ministers to implement a ban on under-18s using sunbeds immediately, and to close salons that are not supervised by trained staff.
In Wrexham, the council currently operates five sunbeds, one at Wrexham Waterworld, two at Queensway Stadium and a further two at the Plas Madoc leisure centre.
Despite a commitment to remove sunbeds from its operations in April next year, the BMA Welsh secretary, Richard Lewis, was highly critical of Wrexham's current situation.
During the debate the Health Minister Edwina said that she was committed to banning the use of sunbeds for under 18s as well as banning unregulated salons.
As a result they recommended that the government sought legislative competence so that they could introduce new laws to ban under 18s from using sunbeds in Wales.
Regulation on sunbeds came into force in 2009, but the researchers suggest stricter control measures are required to prevent an increase in the number of skin cancers.
Janice Smyth, director of the Royal College of Nursing in Northern Ireland, said nurses witnessed the needless death and suffering of cancer caused by the use of sunbeds.
"Not only is it important in promoting local public health and well-being, it also helps to spread the message about the dangers of sunbeds and UV exposure, " he said.
The researchers from the University of Dundee also looked at the risk of developing skin cancer from sunbeds compared with the risk associated with tanning in the Mediterranean sun.
More recently, the Sunbeds (Regulation) Act 2010 came from a Private Members' Bill from Labour MP Julie Morgan and now bans the use of commercial tanning equipment by under-18s.
"We have also stopped the marketing of sunbeds in our leisure centres which has also had an impact on the income received, " added Ken Danskin, the council's leisure and activity officer.
The bill is designed to prevent people under the age of 18 from using, buying or hiring sunbeds and make sure adults are aware of the health risks associated with sunbeds.
However Dr Roberts said that all sunbed parlours should be staffed and in his written evidence he called for a ban on the use of sunbeds for under 18 year olds.
Sunbeds work by exposing the skin to ultra-violet radiation.
He called for an education campaign warning people of the risks of UV light and said there was a need to look at the access to salons and the regulation and use of the sunbeds.
Cardiff North MP Julie Morgan has put down a Private Member's Bill in Westminster calling for under-18s to be banned from using sunbeds, and for all other sunbed use in Wales and England to be supervised.
In men, 6.1% (9, 600) of cancer cases were linked to a lack of fruit and vegetables, 4.9% (7, 800) to occupation, 4.6% (7, 300) to alcohol, 4.1% (6, 500) to overweight and obesity and 3.5% (5, 500) to excessive sun exposure and sunbeds.
Tom Crossan, chair of the NI Melanoma Strategy Implementation Group, said Northern Ireland had been the first region in the UK where sunbeds had been banned from all council facilities and was leading the way with legislation to regulate the industry.
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