I don't think I have read the same accounts you have. The accounts I have seen don't mention the SAS and the statements issued regarding the detah was not issued by the Special Air Service, was it?

It was reported in the news as the the Metropolitan police force as in this statement. They may recruit from SAS for their fast response teams and their operatives but they are as far as I know not an operative unit under the SAS. SAS is the military special forces in Great Britain.

The Metropolitan police is by far the largest policing force in the Greater London [Map] district and lately incorporated also The Royal Park Constabulary into their forces. But they are not a military branch, they are the civilian police though in certain cases they may definitely make joint operations.

The incident that lead to the unfortunate death of a most likely innocent Brazilian man is now being investigated by the Metropolitan Police Service Directorate of Professional Standards which would correspond to Bureau of Internal Affairs in some other countries.