The 22-year-old finished second behind America's Dana Vollmer in her semi-final in 1:55.54. Italy's Federica Pellegrini set a new world record of 1:53.67 to qualify quickest for the final.
"I was shocked with that time," Jackson told BBC Sport. "I now just want to get in there tomorrow and go quicker, put in a good performance and a good time and then we can have some fun in the (4x200m) relay on Friday."
Michael Rock smashed Steve Parry's British record in the semi-finals of the 200m butterfly.
His time of 1:54.58 knocked one second off the previous best to qualify sixth fastest for the final.
"I paced the race a lot better," he said. "It's my first major final so I'm really looking forward to Wednesday night.
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