The visitors require 229 runs, with eight wickets remaining, if they are to win the first Test of the series.
England will 'roll up their sleeves' as they chase Sri Lanka
Graeme Swann is confident England can achieve their highest ever fourth-innings chase, declaring: "history is there to be rewritten".
England need to reach 340 to win the first Test against Sri Lanka, eight more than their best successful chase against Australia in 1928.
Swann has little regard for past form, though, and expects his side to record a famous win when they resume this morning on 111 for two, with Jonathan Trott and Kevin Pietersen at the crease.
"I'd say we're just favourites," he said.
"I don't like statistics. Just because somebody won a game in 1912 chasing 290 or someone got 350 in the Kerry Packer era doesn't mean anything. This is 2012. History is there to be rewritten.
"I don't think we need any genius, I think we just need a bit of good old fashioned rolling your sleeves up and getting your head down.
"The way KP [Pietersen] and Trotty batted at the end is exactly what we need to do [today]. They got their heads down, they kept out the good ones, they made batting look as serene as it's going to get out there.
"People who actually apply themselves are hard to shift on that pitch."
Swann, who had completed his 12th five-wicket haul yesterday, is England's most ready optimist but even he acknowledged a sense of frustration had crept in at the end of the Sri Lanka innings.
The last two wickets yielded a total of 87 runs, with 46 added after a no-ball denied Stuart Broad the final scalp.
"Sure there have been moments of frustration," he said.
"That next 40 minutes [after the no-ball] hurt a little bit. You're looking at a chase of 285, 290 and thinking 'we're going to win this'. At 340, you think it's maybe tipped back to a 50-50 game.
"Those 40-odd runs were very hot and bothering for all the fielders, as you saw because we were at each other's necks by the end."
Swann believes England's first-innings performance - they mustered just 193 between them on a pitch from which Mahela Jayawardene had milked 180 - will inspire them to do better this time.
"We're all disappointed with the first innings. To make the whole innings last 40-odd overs just wasn't acceptable and that's not just the top six, that's all 11 players.
"But the way we bounced back from that proved this team doesn't dwell on things that are in the past. We probably had our best session of the winter after that, getting five wickets. That's a signal of the strength of this team."
Prasanna Jayawardene, the Sri Lanka wicketkeeper who made a momentum-shifting half-century at the end of the Sri Lanka innings, is confident that the hosts can see off England for a second time.
"We have the psychological advantage because they need to score more than 300," he said.
"We have to be patient and do the basics well to get wickets in the morning.
"We have a big chance but we have to come out and bowl well in the morning."
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