Sri Lanka were 112 for three wickets after England declared their innings on 377 for eight at the close of the fourth day of the third and final Test on Sunday.
Earlier, Ian Bell scored his third hundred in his last five Test innings to help England to a first innings lead of 179 over Sri Lanka on Sunday.
After England had declared on 377 for eight, Sri Lanka reached 14 without loss at the break. Tharanga Piranavitana was dropped on five by wicketkeeper Matt Prior, who could not hold on to a diving leg-side chance off Chris Tremlett's bowling.
England declared half an hour before the interval with Bell recording a chanceless 119 not out. He passed 50 for the fifth consecutive occasion in a Test after his team mate Alastair Cook had equalled the English record with six on Saturday.
Eoin Morgan contributed 71 in a stand of 137 with Bell, who faced 169 balls and plundered 12 fours. That stand all but ended Sri Lanka's hopes of claiming the win they need to draw the three-Test series.
Bell's 14th Test century is part of an impressive sequence starting with 115 against Australia in Sydney, 103 not out at Cardiff in this series, then 52 and 57 not out at Lord's.
Bell's classy effort was also the first Test century scored at The Rose Bowl, which is hosting its debut Test match. He reached his laTest hundred with a single that he hooked to deep midwicket off Suranga Lakmal's slow bouncer.
Bell was rarely in trouble. He caressed one drive perfectly between mid-off and short extra-cover for four to go to 62 after reaching his 50 with a sweetly timed boundary, a late cut off Lakmal between second slip and gully.
Morgan survived an lbw appeal by Lakmal when on 58 after he reviewed umpire Rod Tucker's initial out decision. Replays showed the ball pitching outside leg stump.
Morgan, who scored unbeaten centuries in his last two internationals on the ground, began uncharacteristically slowly before accelerating. He had faced 110 balls when he edged Lakmal to the wicketkeeper while advancing down the pitch.
The declaration came after Prior and Stuart Broad were each dismissed without scoring.
England earlier resumed on 195 for four. Sri Lanka claimed just the one wicket in the morning session, that of nightwatchman James Anderson for 27 off 33 balls.
Anderson needed to go on to the attack with England seeking to push on for a victory and he did not disappoint, scoring boundaries off the third and fourth balls of the morning.
First, he elegantly drove Thisara Perera off the back foot through cover and then edged him between second slip and gully.
The left-hander would have eyed a Test best score but did not manage to better his 34 against South Africa in 2008. He edged left-armer Chanaka Welegedera to wicketkeeper Prasanna Jayawardene after cutting him for four the previous ball.
Rain has so far robbed the game of 155 overs while the forecast for Monday is not good.
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