England are thrashed after failing to follow Cook's example

England are in trouble. The depth of their difficulty was disguised but could not be concealed by their captain Alastair Cook's second one-day hundred yesterday.

Cook played with typical fortitude and offered a vigorous retort to those who suggested he was not the man for the job. But the side he leads succumbed to their second successive defeat in the one-day series against Sri Lanka.

Despite an absurd finale, when the tourists utterly forgot that the team's needs always come before those of the individual, England were taught another lesson in the rudiments of the one-day game.

How quickly and thoroughly they undertake a course of further study – and extra prep, cramming and specialist tutors seem to be required – may be the key to Cook's tenure. On the evidence presented in the second and third matches, it seems a distortion of reality that England managed to win the first, although then the weather played its part.

It is hardly helpful that there are other matters to ponder. Shortly before the match began, it was announced that Stuart Broad, the vice-captain and captain of the Twenty20 team, had been punished for showing serious dissent at an umpire's decision in the second match at Headingley last Friday.

Broad disagreed with Billy Bowden's verdict in turning down a lbw appeal late in Sri Lanka's innings and continued to make his feelings clear as the teams left the field, making "offensive and unacceptable remarks" to the umpire. This might not have hindered the team's preparations but it bespeaks a player temporarily out of sorts, which can have a debilitating effect in the dressing room.

England were defeated by six wickets, the sort of margin that was almost inevitable after their total of 246 for 7 in conditions that demanded and deserved at least 30 runs more. That England confounded their felony by being too imprecise, especially in length, eased Sri Lanka's task.

Mahela Jayawardene was again in sumptuous touch, caressing 79 runs in 77 balls before, mind-bogglingly, he sliced a long hop to point.

Dinesh Chandimal, who may one day assume Jayawardene's mantle, saw it through, which was particularly valiant considering that England peppered him with short stuff attempting to exploit a palpable weakness.

But, towards the end, when his hundred seemed less imminent than the target being attained, he and Angelo Mathews conspired to refuse singles to try to ensure Chandimal achieved his personal landmark. He did so with his second six but, whatever the significance of the milestone, it was missing the point.

England must begin addressing their batting order and perhaps the selectors should make that an order. Cook's 119 from 143 balls, which included 13 fours and 57 singles, was adequately paced but he lacked competent support for any length of time. It remains the case that, in most one-day matches when a player makes a hundred, their side wins – but that presumably depends not only on none of the opposition making a hundred but also on the other ten making more than 127 between them.

After the first ten overs, a crucial part of any one-day innings, England were 32-2, Sri Lanka 61-1. The figures tell their own story. Briefly, when Kevin Pietersen was in, making 41 from a partnership of 49 with Cook for the third wicket, there was a chance that England might set a target which, if not exacting, might not be a doddle.

But Pietersen, as so often in one-day cricket in the recent past, holed out when he misread a ball from Jeevan Mendis, the third time in three innings in the series that the bowler has taken the batsman's wicket.

Since Pietersen lost the captaincy, his one-day batting average is slightly under 22 runs per innings.

But Pietersen is merely part of the problem – he is far from being the whole of it.

With Cook back in the side, it makes the presence of Jonathan Trott at number three much more conspicuous. It makes Craig Kieswetter's job as the big hitter – and do not forget that Kieswetter is still learning his trade – far trickier.

Trott was heroic during the winter and virtually carried the batting both in the Australian limited-overs series and the World Cup, but he does not play big shots.

There was an element of recognition that he needs to force the pace in Trott's early dismissal yesterday, driving much more in hope than expectation, the shot swirling slightly embarrassed to mid-off.

A burden was immediately placed on Pietersen as he walked out. Nothing alters the best-laid plans than the loss of wickets, of course, but England were again outsmarted by Sri Lanka's slow bowlers in the middle of the innings, as well as by Tillakratne Dilshan's regular changes of bowling. They scored for 15 overs almost exclusively in singles but there were not enough of them.

After Eoin Morgan was leg before to Mendis, Ian Bell continued his struggles at number six.

No player has looked in such resplendent form in England's Test side in the past six months but, in trying to convert Bell to a one-day number six, a position often demanding distinctive skills, they are in danger of making a sow's ear from a silk purse.

Bell made 30 from 46 balls but he never settled. There are some similar features between him and Jayawardene and there is a strong case for Bell going up the order to three or four and merely playing as he does best.

Cook probably suspected the worst and will have known that England needed early wickets to try to undermine Sri Lanka's challenge. It meant that they had to go searching for them and, perhaps in doing so, they lost a little of the discipline. It was all to Jayawardene's liking and he romped graciously to his 50 from 45 balls, playing exclusively authentic shots.

England's management will presumably have strong words with Broad. He has sailed close to the wind too often before and, when he was handed the responsibility of captaincy, conceded that he would need to amend his behaviour, though added that he improved considerably in the last year. Swearing at the umpire as the teams leave the field was asking for trouble. It is all around.

Lord's scoreboard

Third one-day international: Sri Lanka beat England by six wickets

England won toss

ENGLAND

Runs 6s 4s Bls Min

*A N Cook run out 119 0 13 143 206

†C Kieswetter c Lakmal b Malinga 3 0 0 13 22

I J L Trott c Dilshan b Lakmal 2 0 0 13 16

K P Pietersen c Randiv b Mendis 41 0 6 43 42

E J G Morgan lbw b Mendis 4 0 1 7 5

I R Bell c Kulasekara b Lakmal 30 0 0 46 61

T T Bresnan b Malinga 26 0 1 29 49

S C J Broad not out 1 0 0 2 5

G P Swann not out 11 1 1 4 1

Extras (b4 w5) 9

Total (for 7, 50 overs) 246

Fall: 1-18, 2-30, 3-79, 4-85, 5-157, 6-232, 7-234.

Did not bat: J M Anderson, J W Dernbach.

Bowling: A D Mathews 1-0-4-0, S L Malinga 10-1-54-2, K M D N Kulasekara 10-1-40-0, R A S Lakmal 10-0-62-2, B M A J Mendis 10-0-40-2, S Randiv 8-0-33-0, S H T Kandamby 1-0-9-0.

SRI LANKA

Runs 6s 4s Bls Min

D Jayawardene c Morgan b Dernbach 79 0 9 77 106

*T M Dilshan b Bresnan 3 0 0 6 15

L D Chandimal not out 105 2 11 126 195

†K C Sangakkara c Morgan b Swann 25 0 2 47 58

S H T Kandamby lbw b Swann 11 0 1 13 22

A D Mathews not out 1 0 0 21 22

Extras (lb7 w18) 25

Total (for 4, 48.2 overs) 249

Fall: 1-21, 2-133, 3-194, 4-230.

Did not bat: B M A J Mendis, K M D N Kulasekara, S Randiv, S L Malinga, R A S Lakmal.

Bowling: J M Anderson 9.2-0-55-0, T T Bresnan 9-0-48-1, S C J Broad 10-0-52-0, J W Dernbach 10-2-55-1, G P Swann 10-0-32-2.

Umpires: B F Bowden (NZ)and N J Llong.

Sri Lanka lead five-match series 2-1.