But that prospect evaporated as Kevin Pietersen, Ian Bell, Eoin Morgan, Cook, Steven Davies and finally Broad failed to cash in on what looked an obvious opportunity to prosper.
Cook fared by far the best in a 121-ball innings which contained 14 fours, but no one else could reach 20. Fast bowler Hamid Hassan suffered a nasty injury chasing to the boundary to try to cut off the four which brought up the opener's 50, and would play no further part in the match.
England agreed Ireland spinner George Dockrell could replace Hassan for the second innings, after the Afghan seamer had pitched over a picket fence on the boundary and collided with concrete and metal runners around the sightscreen. He was eventually cleared of serious injury following a trip to hospital on a stretcher.
His absence had no bearing on England's troubles, although before lunch there was barely a hint of the collapse to come.
The only alarm for Cook came when Boyd Rankin discomforted him with a well-directed short one early in his innings.
The left-hander got in a tangle and was unable to get the ball effectively to ground, but no short-leg had been posted at that stage.
Soon afterwards Andrew Strauss pulled Hassan into the hands of square leg, and Jonathan Trott had only a single when he got a faint edge down the leg-side to be caught behind.
A watchful Pietersen needed 10 balls to get off the mark, but did so with a trademark big stride for a four through midwicket - and the rationale was that England needed only patience, on a slow but benign surface, to gradually take control.
Instead Pietersen nibbled an outside edge off Rankin soon after lunch, and Bell's attempt to glide runs behind square off his Warwickshire team-mate resulted in another catch behind when the 6ft 9in Irishman found extra bounce.
Then Morgan edged a Mohammad Nabi off-break to slip, and Cook toppled over and poked the blade down leg to be caught behind off Christi Viljoen.
Scotland off-spinner Majid Haq took a wicket with his first delivery - Davies lbw pushing forward - and Broad then unluckily picked out silly mid-off when he timed a back-foot shot off Nabi. Graeme Swann and James Anderson avoided any more losses until, five minutes before the scheduled tea break, Strauss chose to declare almost 100 runs in arrears.
There was partial vindication when, as in the first innings, Broad and Anderson served up useful new-ball spells as the Combined XI were reduced to eight for three this time.
After Will Porterfield and Paul Stirling's ducks, the two Irish openers had mustered only eight runs between them in four attempts. Porterfield nicked a catch behind down the leg-side off Anderson, and Broad pinned Stirling lbw.
Saqib Ali soon edged an attempted push-drive behind off Broad, and Craig Williams chipped a catch to cover off Swann.
But a stand of 40 between Kyle Coetzer and Mohammad Shahzad ended only when the former played on to Anderson, as the equations began to narrow for an England victory in this first warm-up match for the Test series against Pakistan.
Scoreboard (after day two):
ICC Combined XI 1st innings
281 (C. Viljoen 98, Mohammad Shahzad 51, B. Rankin 43; S. Broad 3-42, G. Swann 3-99)
England 1st innings
Strauss c Haq b Hassan 17
Cook c Shahzad b Viljoen 76
Trott c Shahzad b Hassan 1
Pietersen c Shahzad b Rankin 15
Bell c Shahzad b Rankin 3
Morgan c Stirling b Nabi 1
Davies lbw b Haq 12
Broad c Porterfield b Nabi 19
Swann not out 14
Anderson not out 12
Extras: (b8, lb4, nb 2, w1) 15
Total: (for eight wkts dec) 185
Fall of wickets: 1-44 (Strauss), 2-54 (Trott), 3-107 (Pietersen), 4-121 (Bell), 5-126 (Morgan), 6-132 (Cook), 7-159 (Davies), 8-159 (Broad).
Bowling: Hassan 11-4-26-2 (w1), Viljoen 11-1-42-1 (nb2), Nabi 14-3-42-2, Rankin 16-3-49-2, Haq 3-1-14-1
Overs: 55
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Combined XI 2nd innings
Porterfield c Davies b Anderson 0
Stirling lbw b Broad 0
Coetzer b Anderson 31
Saqib Ali c Davies b Broad 2
Williams c Bell b Swann 11
Mohammad Shahzad not out 34
Mohammad Nabi not out 9
Extras: (lb1, nb2) 3
Total: (For five wkts) 90
Fall of wicket: 1-0 (Porterfield), 2-2 (Stirling), 3-8 (Ali), 4-31 (William), 5-71 (Coetzer).
Bowilng: Anderson 12-6-29-2, Broad 9-5-15-2 (2nb), Swann 10-1-33-1, Finn 6-3-12 0
Overs: 37
