Cook opened at Lord's in the first test draw with scores of only 17 and 28, his lack of runs continuing from the Ashes whitewash in Australia.
But Cook can draw on the memory of his most recent test century at Headingley over a year ago against New Zealand in his search for an elusive ton when the second test starts on Friday.
"I need to get back to scoring as many runs as I can," Cook said. "I'm doubly determined to get a score. I'm doing all the hard work."
"To look at those numbers and see some of the names that you're with - I can't believe it really," Bell said. "When you start, you never really dream of getting this far."
Sri Lanka captain Angelo Mathews rejected the idea that drawing the two-test series 0-0 would be an achievement for his side, and is instead targeting a first-ever test series victory in England.
"It's going to be our last game in England for the summer and we look forward to giving them a good fight and hopefully win it," Mathews said. "We will go out there and play positive cricket."
"The way we fought and the way the boys showed their character was good," he said. "But with our bowling, batting and fielding we still can improve, in all three departments." Sri Lanka has been forced into a change, with regular wicketkeeper Prasanna Jayawardene out with a finger injury.
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