The 15 were freed last Thursday after being seized by Iranian forces in the Shatt al-Arab waterway between Iraq and Iran.
Iran said they were detained for entering its waters illegally, Britain said they were in Iraqi waters.
Several of the sailors and marines, particularly the only woman among them, Faye Turney, have become well known after they were shown repeatedly on Iranian television during the standoff.
On their return to Britain, the personnel said that in Iran they had been blindfolded, bound, kept in isolation and told that they faced up to seven years in jail.
William Hague, foreign affairs spokesman of the opposition Conservative party, said the armed forces would gradually lose dignity and respect if military personnel were allowed to sell their stories whenever they had been in a difficult situation.
Hague said: "There are incredible acts of heroism ... on a weekly, daily basis sometimes in operations in Afghanistan and Iraq but they are not written about."
Menzies Campbell, leader of the opposition Liberal Democrats, predicted a public backlash against the decision to let the personnel sell their stories because in the same week they came home safely, six more British soldiers were killed in Iraq.
Bob Stewart, a colonel and former commander of British peacekeeping forces in Bosnia, said the decision to let them publish was unprecedented and called the capture "hardly one of the most glorious annals of royal naval history".
Max Clifford, Britain's best-known celebrity agent, said letting the sailors and marines tell their story was "purely a propaganda exercise".
Clifford said: "The ministry of defence are very keen for them to do it ... the public are more likely to believe them than they are the ministry of defence or the politicians."
Defending itself in the face of the outcry, the ministry of defence said on Sunday it had granted permission to ensure the navy and the ministry "had sight" of what the former detainees were going to say.