The bands that were part of the 1960s British Invasion were The Rolling Stones, Moody Blues and the Kinks. Chicago was an American band, not British; and The Police, although British, was not from the 1960s but the 1980s.
The British Invasion was the predominant musical movement in the United States towards the middle of the 1960s, when rock groups from the United Kingdom reached high levels of popularity following the success of the British rock group The Beatles. All these groups, clearly influenced by American rock and roll, blues and rhythm & blues, were able to elaborate simple and catchy songs.