The Chilcot inquiry was expected to take a year to report when it was announced by the government six years ago. It is looking at the decisions made in the run-up to the start of the war in 2003 and Britain's involvement.
Earlier this month, Prime Minister David Cameron criticised the delay to the probe, led by former civil servant John Chilcot, saying he wanted to see a timetable for publication.
A total of 179 British soldiers died in the conflict in Iraq between 2003 and 2010.
Matthew Jury, the lawyer representing the families, said there had been "outrageous delays" so far and voiced concern that these could be "interminable".
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"The families are not content to simply wait forever for the inquiry to give a publication date and if Sir John does not impose... A deadline for publication, then we'll be seeking judicial redress," Jury told BBC radio.
"Iraq bubbles up in the headlines over the years and it's like an open wound continually prodded," he added on BBC radio.
"The only way for me to move on from this now is to consign Iraq to history and part of doing so is to get this inquiry published."
Chilcot insisted last month that his probe was making "significant progress" but could not give a timetable for publication.