A spokesman for the Criminal Cases Review Commission (CCRC) has said: "We are told by lawyers representing [the men] that an application is imminent."
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A year ago the International Court of Justice ruled that Japan's decades-old whale hunt in the Antarctic should stop.
Shadow chancellor John McDonnell has backed a free vote for MPs on the issue.
Savers into the new scheme can expect rates as high as 4 per cent from some banks.