Jersey has 'very serious' drink and drug problem
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He wants an extra £100,000 to be given to the service because it is "swamped and needs more resources".
But the Council of Ministers has opposed the senator's call for more funding.
It said the availability and affordability of alcohol in the island needed to be addressed.
Senator Shenton said there were an estimated 7,500 people - about 8% of the population - who drank too much in Jersey, along with about 800 heroin users.
'Particularly worrying' He said: "Teenage girls in Jersey drink far more than their UK counterparts which is particularly worrying when you visit the UK and see how much they drink over there.
"Children as young as 13 and 14 are going out in Jersey, getting drunk and passing out."
The Senator did not think the Council of Ministers idea of raising the price of alcohol would work.
"I don't think adding 20p to a bottle of alco-pop or £1 to a bottle of wine is actually going to make any difference whatsoever," he said.
He added: "The Council of Ministers said we will stop the source but the source in many cases is their own home, where they take alcohol from their parents.
"And I know of parents who actually give alcohol to 14 and 15 year old children."
The Council of Ministers said: "Simply investing in (alcohol) health services needs to be matched by whole population preventative measures."
And added: "It is worth noting that the Alcohol and Drug budget is not the only funding source that is specifically directed at tackling the problems of substance abuse and the harm it causes."
The proposal was due to be debated in the States this week.