"Milk producers are not going to say no to extra quota," stressed Union spokesman, Joe McDonald.
"It's only natural that every dairy farmer wants to produce more milk.
"However, the Union has assessed the current state of international dairy markets. And the clear conclusion reached is that it could take very little extra milk to bring significant downward pressure on producer prices.
"The experience of recent months confirms just how volatile international markets for milk products really are at the present time."
Looking further ahead, the Union holds a similar view regarding the Commission's specific Health Check proposal to introduce phased increases in milk quota up to 2015, at which stage they will be done away with entirely.
"We do not want to see any steps taken that will reduce farmgate milk prices," explained Joe McDonald.
"The Commission has two proposals on the table regarding the future of milk quotas. One is to go for the soft landing approach: the other is to maintain the status quo and simply terminate quotas at the end of March 2015.
"The Union feels that the latter approach will help stabilise European milk prices over the coming years.
"And, in reality, no one knows what state international dairy markets will be in come the beginning of 2015."
The Union spokesman went on to point out that local dairy farmers will still have access to quota in Great Britain, irrespective of what decisions are taken courtesy of the health Check negotiations.
EU Farm Commissioner, Mariann Fischer Boel, expressed her delight at the decision taken by the Council of Agriculture Ministers.