Strength of character wins World Cups and Ben Ryan's England showed character in spades after bouncing back from a near embarrassment in yesterday's first pool match against Tunisia. By the end of the day they had people talking about them again as possible world champions after a clinical 26-7 win in their final game against Kenya, a strong sevens side, which secured a quarter-final today against Samoa.

Upsets can happen in sevens but Tunisia were never seriously expected to push England all the way. When Tom Varndell sprinted clear down the left wing to score in the first minute of the second half, it gave England a 19-point lead over the African team and the win seemed a formality. Unwisely, England let their attention wander and while they were napping Tunisia strolled in for three tries.

“We were a bit lackadaisical and didn't stick to the game plan,” Ben Gollings, the veteran England fly half, said. “We missed tackles that we usually make.” For the second game in a row, Varndell scored with his first touch against Tunisia, using a change of pace to draw the defence and then leave them standing. It put England ahead after only 30 seconds and Varndell could have scored with his third touch five minutes later when, having crossed the tryline, he decided to pass the ball to Gollings for the scoring honours.

It was a selfless act, but also a sensible one. Gollings touched down by the posts, giving an easier conversion that ultimately proved crucial.

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England did not seek to make excuses after the narrow win, but the harsh morning heat probably affected them badly. Varndell and Rob Vickerman were both sick before the match and the players left the field looking drained. In the cooler evening air, they performed better against Kenya.

Varndell failed to complete a hat-trick of scoring with his first touch in a pool game, although it looked on when he burst through the middle only to trip on a blade of grass in the pay of Kenya.

He did get his fifth try of the tournament, with a sprint in from 60 metres, but England's key man was Isoa Damudamu, the Fijian-born flanker, who showed his strength by twice rampaging through the defence to score. His first try was achieved with a defender clinging to his ankles and two more round his shoulders.

“This team is assembled for big games,” Ryan, the head coach, said. “This is what they do well at. We didn't let them get into their stride and we suffocated them.”

They will be joined in the last eight by Wales who qualified as one of the two best pool runners-up after keeping Argentina to a 14-0 win in their deciding match. Wales play the ominous-looking New Zealand today, with the winners to play England should they beat Samoa, while Kenya, who finished on the same points difference as Wales, play Fiji.

The biggest cheer of the day from the 40,000-strong crowd came for Ireland who won a rollercoaster lunchtime game against Australia 24-21. Ireland, semi-finalists in the first World Cup Sevens in 1993, rarely play on the world sevens circuit these days but they got off to a flying start against the Wallabies, racing to a 17-0 lead.

Australia regrouped and moved ahead 21-17, but in the dying seconds of the match, Gary Brown came into the line at speed and scored the winning try.

Scotland's hopes of reaching the Cup quarter-finals vanished in the first half of their opening pool match on Thursday when they fell 33-0 behind to Canada before half-time, but they showed a lot of spirit in their final pool match with South Africa, who play Argentina today.

The Springboks would have been knocked out if Scotland had won and when Ryno Benjamin was sent to the sin-bin for stupidly slapping the ball away after Scotland were given a penalty with his side only 14-7 up, the look on the face of Paul Treu, the Springboks coach, was thunderous. Scotland duly took advantage of the extra man to draw the scores level but they could not find a third score and South Africa put matters out of doubt with their own try in stoppage time.

England's women began their World Cup in the most dominant fashion, without conceding a point in three games, although they will not feel complacent as New Zealand's defence also remained intact.

Sue Day, the England captain who came out of retirement for this tournament, led by example, scoring two tries in each of the first matches as the United States, a potential banana skin, and Russia were beaten 17-0 and 29-0. England's final match was even more impressive, with Japan capitulating 47-0.

England play Australia in today's quarter-final and Simon Amor, the head coach, said: “We have worked very hard on our defence and that certainly showed.”