His comments came as legal teams for key parties were allowed to read statements to the inquiry.
It has already heard of the abuse Mr Mousa and his fellow detainees suffered.
A short video showing Cpl Donald Payne shouting obscenities at the hooded Iraqi prisoners calling them "apes" has also been played.
In 2007, Cpl Payne was jailed for a year and dismissed from the Army after being convicted of war crimes charges related to the death.
On Monday, Mr Singh told the inquiry: "The official version of events was that nothing on that video was in fact illegal.
"What we saw was a soldier trying to implement official policy, forcing detainees to get back into stress positions when they were clearly moaning and unable to maintain those positions.
"They are all shown hooded, again in accordance with orders, again illegally."
Mr Mousa and nine other civilians were arrested at a Basra Hotel on 14 September 2003 by soldiers from the former Queen's Lancashire Regiment who found weapons on the premises.
Staff insisted the weapons were kept for security, but they were taken to a detention centre at the Battle Group Main camp, under suspicion of being insurgents.
Two days later Mr Mousa was dead. A post-mortem examination showed he suffered asphyxiation and had at least 93 injuries to his body, including fractured ribs and a broken nose.
Lawyer Phil Shiner: "Baha Mousa was a father of two young children, now sadly orphans"
Mr Singh said: "One of the striking features of the terrible events is that the abuse did not take place in a secret location behind closed doors.
"The temporary detention facility (TDF) was open to the outside. Many people must have seen or heard what was going on. Many seem to have visited the TDF.
"This gives rise to serious questions about the professionalism of the outfit and whether the culture was one of impunity, [and] about the capacity of the regiment's members to question and challenge abuse."
Convicted war criminal
A six-month court martial saw seven soldiers facing war crimes charges relating to Mr Mousa's death.
In April 2007, all but Cpl Payne, 36, were cleared on all counts at Bulford Camp in Wiltshire.
He became the UK's first convicted war criminal under the International Criminal Court Act.
The brutality was completely unacceptable. It has stained the reputation of the British army
David Barr MoD counsel
In July 2008 the MoD agreed to pay £2.83m in compensation to the families of Mr Mousa and the nine other detainees.
David Barr, counsel for the Ministry of Defence, said the "appalling" behaviour of British soldiers in the case "disgusted" the Army.
He told the inquiry: "It is with huge regret that the Ministry of Defence acknowledges the way in which some of those techniques were used on Baha Mousa and those detained with him.
"The brutality was completely unacceptable. It has stained the reputation of the British army."
Cpl Payne's barrister, Michael Topolski QC, said the former soldier hoped the inquiry would provide a "clearer and fuller picture" of events.
Mr Topolski said: "Donald Payne has accepted and he does accept that he violated his duty to those detainees.
"For that, through us, now without hesitation he wishes to publicly apologise to each of them and in particular to the family of Baha Mousa."
The inquiry later adjourned for the day and will reconvene at 1000 BST on Wednesday when the first witness will be Mr Mousa's father.
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