More than 1,000 members of the British military have deserted since the start of the Iraq war, the BBC has learned.
Cases of soldiers deserting the army are said to be rising
Figures for those still missing are 86 from 2001, 118 from 2002, 134 from 2003, 229 from 2004, 377 from 2005, and 189 for this year so far.
The news comes as Parliament debates a law that will forbid military personnel from refusing to participate in the occupation of a foreign country.
The MoD insists "absent without leave" figures have remained constant.
A Ministry of Defence spokeswoman said the soldiers currently missing were considered to be "absent without leave" and would have to be court martialled before they could be found guilty of deserting.
She added only one person has been found guilty of deserting the Army since 1989.
According to MoD figures 2,670 soldiers went "absent without leave" in 2001, with the figure rising to 2,970 in 2002 and falling in 2003 to 2,825. In 2004 it rose to 3,050, falling back again in 2005 to 2,725.
She added: "We regard that figure as fairly constant. It often happens for family reasons and there is no evidence to suggest operational commitments contribute significantly to the figures."
John McDonnell, Labour MP for Hayes and Harlington told, Parliament last Monday that the number of absconders had trebled since the invasion with more soldiers "questioning the morality and legality of the occupation".
On Sunday he insisted the numbers of British troops trying to absent themselves from service in Iraq were rising.
"My understanding is there are a lot more seeking to avoid service, through different mechanisms," he said.
"I think what the MoD is saying flies in the face of all the other evidence and the experience of soldiers on the ground."
But former defence minister Don Touhig told BBC Radio Five Live there were no "hard facts" to suggest the Iraq conflict was prompting increased numbers to leave the forces.
Justin Hugheston-Roberts was the solicitor for Flight Lieutenant Malcolm Kendall-Smith who was sentenced to eight months in prison for refusing to follow orders in connection with a deployment to Iraq.
He said: "I am approached regularly by people who are seeking to absent themselves from service. There has been an increase, a definite upturn."
Military law expert Gilbert Blades, who represents soldiers at courts martial, said the numbers leaving because of Iraq were often obscured as they were not counted as conscientious objectors.
"One can't help thinking that what's behind every absence is the problem in Iraq and I would think that if the real truth was told, then the Iraq problem has contributed to a huge number of people going absent," he told BBC Radio Five Live.
Former SAS member Ben Griffin was allowed to leave the military after telling his commanding officer he was not prepared to return to Iraq because of what he believed were illegal acts being carried out by US forces.
Mr Griffin would never have considered deserting but says his views are shared by many others in the British military.
He told the BBC: "There's a lot of dissent in the Army about the legality of war and concerns that they're spending too much time there."
Major General Patrick Cordingley, who commanded the 7th Armoured Brigade "Desert Rats" in the first Gulf war, said servicemen's views on Iraq prompted some to leave but "good leadership" would stop it reaching epidemic proportions.
He said those who had been to Iraq before or whose families were unhappy about them going were among those who might not want to serve there.
"If you have such a person in your unit you have to discuss things with them... you do not necessarily want people with you if they have that particular view," he added.