David Willey bowled his way into ­England’s World Cup squad with a ­display of nerveless death bowling but, even with his feet up in the dressing room, Jofra Archer confirmed his ­importance to this side.

As Pakistan threatened a remarkable run chase after Jos Buttler had scored England’s second-fastest ODI hundred, Willey showed his mettle just when captain Eoin Morgan needed one of his seamers to deliver. Willey gambled on pulling off his yorkers, taking two for 13 in his final two overs as Pakistan lost by 12 runs having looked well placed with five overs to go.

But apart from Willey, England’s quick bowlers struggled and the attack lacked penetration without Archer’s pace as Fakhar Zaman matched ­Buttler’s strokeplay with his own ­brilliant hundred.

Resting Archer confirmed he has done enough to be in the final World Cup XV, but for seamers such as Liam Plunkett and Willey this was an important chance. Plunkett lacked penetration while Chris Woakes appears short of fitness. Woakes has done enough in the past to be certain of a World Cup berth. Plunkett is now fighting with Tom Curran for the final slot.

It was a flat pitch, with no help for the bowlers, but that is what will be produced for the World Cup and only serves to show the importance of raw pace. Without Archer, England’s attack was one-dimensional and predictable, thankful they had the weight of runs on their side.

Buttler celebrated his eighth ODI century by rocking his bat in his arms in recognition of the birth of his first child two weeks ago and for England batting against a Pakistan side without their star leg-spinner Shadab Khan, who is recovering from hepatitis, was child’s play.

A fifty for Jonny Bairstow in his first innings of the summer, Jason Roy’s 87 on his return to action from a back injury and Eoin Morgan’s 71 off 48 balls meant England did not need to call on the likes of Ben Stokes and Moeen Ali. 

This was the 35th time in 82 innings since the last World Cup they have ­broken through 300. To put that in ­perspective, England managed only 300 or more 34 times in their entire one-day history up until 2015.

Roy took a while to find his timing after a three-week lay off but a six over long-on off Faheem Ashraf settled his nerves and another over extra cover showed that even when his timing is off, he can rely on sheer power to see him through. His dodgy back was tested by Bairstow’s running but they have built a natural understanding and their century stand was their sixth in 25 innings. It left Pakistan having to muzzle England’s gunslingers with wickets in hand.

Bairstow was brilliantly caught on the boundary and while Roy was not at his most fluent, this was important time spent at the crease. A hundred beckoned but a brief rain break disrupted his momentum, and he was caught off a top edge.

Morgan bristled with intent. Joe Root slapped a Yasir Shah long hop to midwicket but England could afford to lose their anchor. It was time to steam away from the opposition. Buttler thrashed Yasir for a six and two fours in three balls; the leg-spinner’s lack of variation making him easy picking for two fine players of spin.

With no reverse swing or turn, ­Pakistan were facing a mauling. They tried cramping Buttler for room, bowling back of a length with the leg-side field pushed back but Buttler got round that by stepping to the onside to hit a slower ball from Ashraf for four. 

Bowling full to Buttler is even more of a gamble. His bat speed and power enables him to smash slower-ball ­yorkers straight into the stands. ­Pakistan bowled 17 full deliveries; ­Buttler smoked them for 39 runs.

The only defensive option was to try to force him to hit to the longer boundary. It did not work for Buttler has the power to clear any rope and he reached his ton with a six over long on. It was England’s second-fastest ODI century behind Buttler’s own record set four years ago against the same team.

For large parts of their reply, ­Pakistan were ahead of the game. Fakhar was brilliant. The first Pakistani to score an ODI double hundred, he carries their World Cup hopes. ­England bowled too short to him, fearful of the straight boundaries, but he had the power to help himself to leg.

Morgan left his seamers on in the middle overs, but England only broke through when Fakhar chased a wide ball from Woakes. Morgan, fielding at extra cover, was the only one convinced he heard the edge and reviewed.

When Babar Azam was out in the next over, the run rate looked daunting but Sarfaraz Ahmed went after Adil Rashid and with 53 needed off five, Pakistan looked favourites. But Willey found the blockhole and England held on.

Wide yorkers will be the default delivery. Hasan Ali drills two to cover off one and, after a debatable wide, slashes a cut to short third man. Sharp stop from Moeen who saves three. Woakes goes seventh-stump to Sarfraz who gropes after it and misses. The Pakistan captain can only chip the fourth ball to point for a single. Pakistan need 14 off two balls. Woakes again finds the extent of the tramline to keep it legal and a dot ball and Hasan squeezes out a single off the last ball. England win by 12 runs.  

Plunkett is back for the penultimate over. He begins with one painting the tramlines and Faheem can only squeeze it out for one. Sarfraz pulls the slow-ball bouncer riskily but it lands between square leg and fine leg and they run three. Faheem sacrifices himself slogging and Pakistan are left requiring 19 from the final over which will be taken by Woakes. Plunkett will not bowl out but trots into the deep with 9-0-64-2. 

Faheem c Stokes b Plunkett 3 Reaching desperation stakes he spoons a length delivery from outside off to midwicket. Easy catch for Stokes. FOW 353/7

Willey shows his mettle and control, restricting them to two and a single, then winkles out Imad. Sarfraz crossed to get on strike and drives the next ball for a single, digging out the yorker. Willey closes it out with a single and a dot ball with his yorker strategy from round the wicket. He finishes with 10-0-57-2. Pakistan need 27 off 12. 

Imad c Buttler b Willey 8 Top-edged a cross bat swipe and Buttler ran back to fly slip and leapt headlong to take the catch. FOW 345/6

Sensational shot from Sarfraz, drilling Rashid's googly through the covers for four. Bairstow makes a terrific diving save on the rope from another cover drive, saving two and then Willey cuts off a pull at midwicket, restricting them to two again. But Imad Wasim thrashes the last ball over long-on for six. Huge over. Rashid ends with one for 81. Pakistan need 32 off 18. 

Asif brings up his fifty with an off-drive for two but expires trying to up the tempo. Enter Imad who bunts two past mid-off helped by a wild throw. Pakistan require 49 off 24 balls. 

Rashid's googly is taken by Sarfraz about two yards outside leg-stump and late cut past the stumps for a single. Asif whips a single off his legs, Sarfraz sweeps two and Asif steps away to cut two. Good stops from Willey and Bairstow stem the wound. 

Willey will have another go at cementing his place in the World Cup squad. He takes an age with his captain to set the field. He comes round the wicket and adopts a full length. Asif digs it out to mid-off. Dot ball. He lands his next attempted yorker, though, too soon and Asif creams it over long off for six. The right-hander swats two through point but Willey fighst back to end with two dot balls. Pakistan need 61 off 36 balls. Morgan has 12 balls from Rashid up his sleeve and brings him back now. 

Woakes has to try to repair the damage inflicted on Plunkett and he does so for four balls until Asif climbs into his wide yorker and creams it through point for four. Pakistan need 69 off 42 balls. 

England have done well this past five overs to rope in the runaway steer and they have done it by holding their nerve. Sarfraz is slowing them down like Root did for England but after Plunkett bangs in a bouncer so loopy it is called wide, the Pakistan captain wakes up and takes his left leg out of the way to smear a length ball off middle over midwicket for four. Plunkett is visibly tired and bowls another wide then Asif thrashes a cross bat hoick past mid-on for four. Good stop by Root at short fine leg turns a four into a single. Pakistan need 78 off 48 balls. 

Sohail's top hand came off the bat when he played the shot. Slower ball from Plunkett? Haris certainly had to overreach for it. The batsmen cross and Asif takes the next ball, working it behind square for a single. Sarfraz, is off the mark with a French/Chinese cut that was  almost a Welsh drag-on. Ten overs to go and Pakistan need 98. 

Moeen is going to bowl out and begins with two dots by virtue of one that was flighted and the other he darted in. Sohail chips two over the infield, the batsmen exchange singles then Haris ends Moeen's spell with a lofted drive over wide mid-off for three. Moeen ends with one for 66. 

Asif Ali smites a six over long on and then chips the next but one ball to mid-on. Willey sprints forward and dives, getting his hands under it and grazing his knuckles on the grass before it spills out. A hard chance but one he should have taken. Willey excoriates himself, stomps about a bit. Rashid looks crestfallen. Pakistan require 107 runs from 72 balls. 

Asif, who has extraordinary power hitting in the arc between the bowler and midwicket, comes down the pitch and blasts it over wide mid-on for six. Stokes reached its destination but it was too high for him to gather. Four singles and a two erode the target score with a handy 12. Moeen has 9-0-59-1 so far. 

Rashid begins with three dot balls and then Asif decides to take him on and swats a shovelly drive over the midwicket sweeper for six. Pakistan need 129 from 84. 

Two new batsmen are the trigger for Moeen to return. Haris Sohail on-drives a single, Asif sweeps another and Haris ends an important over for England with a third single off it. England have clawed it back.  

WICKET! Fifty and out for Babar Azam!Adil Rashid with the wicket, taking a simple return catch as Babar slapped a long hop back at him. Pakistan 233-3.