The increased level of milk imports this year comes despite dairy farmers facing huge superlevy fines.
Preliminary figures from the Department of Agriculture showed that the country was 0.94pc or around 55m litres over quota for 2013/14.
As a consequence farmers are facing a superlevy fine of between €15m and €16m.
At 351m litres, total milk production in the Republic was well up during January and February this year, the Department figures confirm.
Lakelands Co-op and North Cork Co-op have both admitted importing milk from Britain.
In a statement last week Lakelands said the import of milk from Britain increased the efficiency of the co-op's processing facilities.
"Lakeland Dairies is a cross-border co-operative, with operations North and South.
"From time to time and occasionally, the co-op purchases milk from Britain to complement its processing efficiencies," the statement said.
North Cork chief executive Pat Sheahan said an investment by the co-op in a new drying facility had given the dairy additional processing capacity.
He pointed out that the co-op processed 90m litres each year but just 37pc of this volume came from its own supplier base.
Mr Sheahan said the import of milk from Britain was a short-term measure.
However, with milk supplies in Britain running 13pc ahead of last year's levels, there are growing volumes of milk in the country which dairies do not have the capacity to process.
DAIRIES STRUGGLING AFTER 'WALL OF MILK' HIT
This has resulted in what is described as "distressed" milk being offered to processors in Ireland for as little as 23-24c/litre.
Despite the low price, dairies have suggested that the volume of milk imports was likely to fall sharply this month due to the surge in local milk supplies.
Processors are describing this April as among their busiest ever in terms of milk deliveries.
Supplies are running up to 20pc ahead of last year, with dairies admitting that they are struggling to deal with what has been described as a "wall of milk".
One processor said that milk tankers were "going everywhere and anywhere" in an effort to keep milk collected and processed.
With processors stretched at the moment to deal with milk deliveries, there are fears that they will struggle to cope when supplies peak over the coming weeks.