Cheteshwar Pujara was the highest-placed Indian batsman as he rose a rung to be sixth, while Pragyan Ojha broke into the top-10 among bowlers after gaining one spot to be 10th in the latest ICC Test rankings issued today.
Pujara is the only Indian batsman inside the top-20 of the rankings. Among the bowlers, off-spinner R Ashwin dropped a rung to be eighth in the latest list, while Zaheer Khan is placed 17th.
Bell, who won the ICC Emerging Cricketer of the Year Award in 2006, is now 11th in the rankings for Batsmen, just three ratings points behind New Zealand's Ross Taylor after jumping six spots.
A right-handed batsman, Bell made scores of 109 and 74 in the Lord's Test.
Jonny Bairstow is now just outside the top 50 in 53rd spot after rising 12 places after making scores of 67 and 20.
The batting table is still headed by South Africa's Hashim Amla with West Indies' Shivnarine Chanderpaul in second place and AB de Villiers in third position.
Meanwhile, in the rankings for Bowlers, James Anderson moved up one place to join Peter Siddle in fifth spot, and both the bowlers now trail fourth-placed Saeed Ajmal of Pakistan by 25 ratings points.
England off-spinner Swann, who ended with a match haul of nine for 122 in the Lord's Test, has gained one place and is now seventh, just five ratings points behind Anderson and Siddle.