Grampian Police and Aberdeen City Council Social Work Department yesterday defended themselves against criticism of the handling of the Scott Simpson murder case.

After the court the Simpson's solicitor Mr George Mathers said: ''The family want an inquiry into the circumstances in which someone who has a mind so depraved as to be capable of an act such as this should be allowed not only to be free in the community but even when supervised apparently is allowed to reside in accommodation which overlooks a children's playground.

''They are as concerned and more concerned than the Solicitor General and we heard what he had to say about certain aspects of the investigation.''

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While the police deny making any mistakes the social work department admitted they failed to see Leisk the minimum number of times laid down in Scottish Office guidelines for a Supervised Release Order which he was the subject of - two visits a month - and that the last interview he had was two months before the murder.

They also admitted that the social worker who decided the frequency of visits could be reduced because of Leisk's apparent progress had done so without consulting superiors as laid down in the guidelines.

Grampian Police said all avenues were explored and a third of the force were involved in the search and while lessons can be learned from the tragedy that does not mean mistakes were made. They said well intentioned but false ''sightings'' affected the inquiry.

They do concede that if the officers who searched the bushes where Scott's body was found missed it then that was a mistake but they do not accept the body was definitely there when they searched.

''People rightly ask why Scott's body wasn't found,'' said Assistant Chief Constable Peter Wilson. ''Was he there or was he put there later? ''The answer to that we will never be sure of. Leisk told us he put him there when he killed him on the Thursday afternoon.''

Inspector Kenny Lawson who was in charge of the search said that four search-trained officers had searched the area where Scott's body was found.

''The police officers believe they searched this area thoroughly and specifically recall being within the bushes in the lane.

''Following the discovery of Scott's body and during the increased activity there we had a member of the public come forward and report having seen a man, believed to be Steven Leisk, acting suspiciously at the end of the lane during the Friday evening after the search.

''We have tried to resolve the question as to whether Scott's body might have been elsewhere to remove any uncertainty but we may never know.''

As the search continued police began to check known sex offenders in the vicinity of Scott's home and near the possible sightings which had been received.

Leisk was one of 31 names which emerged and his address was on their records as 9 Bedford Road, a house which does not exist.

Police started to work through them but had not tried to contact Leisk by Monday at 5.40pm when a relative phoned to give them his address and express concern. Less than an hour and half later he was in custody.

Mr Wilson said hindsight changed the view of the circumstances but they had to go on the information available at the time.

He said that had they known that Leisk lived at 98 Bedford Road and not number 9 it would not have prevented Scott's murder but it was possible they would have found him earlier.

Aberdeen's social work director Mr Peter Cassidy said that it was a very experienced social worker who dealt with the Leisk case. He said after his release from prison Leisk worked in groups and individually with the social worker. All the key indicators suggested he was making positive progress.

He kept all his appointments, even keeping one on July 21, four days after the murder. Even at that meeting he gave the impression progress was continuing.

''This tragic case does underline the notoriously difficult task of supervising such people in the community. They present a risk to others but may be plausible and devious.''

Aberdeen Council leader Margaret Smith said the case highlighted the difficulties for those drawing up guidelines for working with sex offenders and said she was satisfied Leisk was being adequately supervised.