The ICMG was formed in 1961 under the command of Group Captain Ian Gilmore, who drafted scientific specialists like scientist Rachel Jensen under the Peacetime Emergency Powers Act. (DW: Remembrance of the Daleks) The Intrusion Countermeasures Group was composed of Royal Air Force personnel and equipment.
The group encountered the Daleks and the the Doctor in 1963, in what became known as the Shoreditch Incident. They were shut down soon after. (DW: Remembrance of the Daleks, MA: Who Killed Kennedy) Journalist James Stevens attempted to investigate and make public information concerning this group, as well as UNIT, but was stymied in doing so. (MA: Who Killed Kennedy)
The Intrusion Countermeasures Group was an arm of the British military, under the auspices of the Royal Air Force, which operated in the mid-20th century. The Group was set up in the mid-1950s in the wake of several worldwide encounters with alien spacecraft, most notably during the Roswell incident of 1947. (Star Trek: Daedalus - Reversed Polarities)
In November 1963 a detachment from the ICG, under the command of Group Captain Ian Gilmore, was ordered to investigate a possible downing of an "unidentified flying object" in the Shoreditch area of London. When Gilmore and his men arrived they discovered a strange alien device in the middle of a scrapyard with a badly injured man lying next to it. After the man, later revealed to be named Mortimus, had recovered he offered to assist Gilmore and the ICG in deciphering the alien devices technology. However, this later turned out to be a ruse, as Mortimus was the alien being who controlled the device and had used the ICG resources to affect repairs on his ship. ("Remembrance")