Steve Thompson, Mark Reagan and Phil Vickery - part of England's 2003 Rugby World Cup-winning squad - former Wales stars Gavin Henson, Colin Charvis and Ryan Jones and England and Lions scrum-half Harry Ellis are some of those seeking damages from World Rugby, the Rugby Football Union and the Welsh Rugby Union for failing to put in place reasonable measures to protect their health and safety.
They believe that the alleged negligence led to long-term neurological complications.
World Rugby, the RFU and WRU have questioned the way the lawyers at the centre of the case have pursued it.
"Throughout the four years this legal case has taken to date, rugby's priority has always been the welfare of the players," they said in a joint statement.
"Whilst we cannot reach out to any of the individual players involved in legal action, what we would want them to know is that we listen, we care and we never stand still on player welfare.
"The delays in this case and conduct of the claimants' lawyers is a great cause of concern. n the interests of the players, we urge Rylands Garth to meet all court imposed deadlines and to present the full details of the case they are making against us.
"Only that way can we move this matter closer to the court hearings which will provide a resolution to this issue, which is surely in the interest of all parties."