The Criminal Cases Review Commission (CCRC) referred the case back to the Court of Appeal in 2001, which upheld the conviction again in 2002. The CCRC rejected further applications from Bamber's lawyers in 2004 and 2012.[3] In July 2013 the European Court of Human Rights ruled in Bamber's favour that there must be a possibility, for whole-life prisoners, of release and review.
Answered my own question. So four appeals have failed ? If Wikipedia is correct.