Having last played for England in 2001 at Lord's against Pakistan, Sidebottom took eight for 86 for the match.
Dwayne Bravo scored 52 Monday, the highest score from any West Indian batsman.
Kevin Pietersen hit a test high 226 as England declared at 570 for seven
The West Indies then made 146 and was forced to follow on. No play was possible Sunday because of rain.
It was the worst ever test defeat for the West Indies, which was lost by
an innings and 237 runs to England at The Oval in 1957.
The West Indies resumed Monday on 22-2, chasing 402 to avoid an innings defeat.
In the third over, Chris Gayle on 13 edged a ball from Liam Plunkett and
wicketkeeper Matthew Prior took a diving catch.
Prior had dropped Gayle on 8 Saturday.
When play resumed after a 150-minute rain delay, Sylvester Joseph (1) was out lbw to Sidebottom, leaving the West Indies on 47-4.
Ten runs later, Devon Smith (16) hit a ball from Sidebottom to Andrew
Strauss in the slips, who fumbled the ball before catching it.
After rain again delayed play for 30 minutes, Dwayne Bravo and Runako
Morton put on 63 runs for the sixth wicket to take the tourists past 100.
Morton (25) was out when he swept a delivery from Steve Harmison up in the air and Prior ran forward to catch, leaving the West Indies at 120 for six.
Bravo reached his 50 before tea and off 63 balls, with six boundaries and
He made two more runs before he was bowled by Monty Panesar.
Harmison then bowled Jerome Taylor for 0.
The West Indies was also without experienced middle-order batsman Shivnarine Chanderpaul, who withdrew with a knee injury.
Monday's play was largely under dark cloudy skies and players wore jumpers due to a maximum temperature of 9 degrees Celsius.
All players wore black armbands and observed a minute's silence in memory of ICC president Percy Sonn, who died Sunday.
The third test starts June 7 at Old Trafford in Manchester.