The visitors lost five wickets in the afternoon session, including the veteran pair of Angelo Mathews and Dinesh Chandimal, and trail by 298 runs.
Olly Stone, in his first test since 2021, picked up his second wicket completing an over he started before lunch, when Pathum Nissanka (12) glanced one to Matthew Potts at leg slip.
Mathews and Chandimal tried to rebuild with a partnership of 48 but a double-wicket maiden from Potts put England on top.
Mathews (22) played around a straight one and captain Dhananjaya de Silva was caught by Harry Brook at second slip for a three-ball duck as Sri Lanka fell to 83-5.
Chandimal (23) then clipped a straight one from Atkinson to Dan Lawrence at leg slip as Sri Lanka slipped further into the mire at 87-6.
Milan Rathnayake (19) counter-attacked until he nicked Chris Woakes to keeper Jamie Smith, leaving Sri Lanka's hopes of avoiding the follow-on with Kamindu Mendis (26 not out).
Sri Lanka lost both openers before lunch, Nishan Madushka (7) chopping a wide delivery from Woakes on to his stumps before Stone removed Dimuth Karunaratne (7) in identical fashion.
England earlier resumed on 358-7 and Atkinson began the day with back-to-back boundaries, clipping Lahiru Kumara's first delivery to fine leg then driving the next through cover.
The 26-year-old was given out lbw from the third ball of an eventful opening over, but was reprieved on review as the ball was travelling down the leg side.
Atkinson moved to 99 with another classy cover drive for four and, unlike Joe Root on day one, needed just three balls to reach three figures with a straight drive to the fence.
Sri Lanka leaked 35 runs off the first five overs before the introduction of Asitha Fernando, who had Potts (21) caught behind by keeper Madushka.
Atkinson fell trying to hit Fernando into the stands, brilliantly caught by Rathnayake on the midwicket boundary for 118 off 115 balls.
Stone (15) was the last man out off Fernando (5-102) as England added 69 to their overnight total.
England won the first test at Old Trafford last week by five wickets. Sri Lanka must win at Lord's to have a chance of winning the three-match series.
--Reuters--
