Alastair has moved up to third ICC Test batting rankings after hitting a career-best 294 at Edgbaston against India.
The England opener has risen eight places in the standings, overtaking team-mates Jonathan Trott and Ian Bell.
Only South Africa's Jacques Kallis and Sri Lanka's Kumar Sangakkara remain above Cook.
Meanwhile, James Anderson maintained his hold on second position in the bowling list, while Stuart Broad has moved up two places to joint fifth with teammate Graeme Swann.
