A brief history

Bangladesh v England

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2003-04 (Bangladesh)
England's inaugural tour of Bangladesh was an unexpectedly tense affair. Though their opposition had lost 23 of their 24 Tests to date, and the majority of them by a country mile, the side was no longer an absolute pushover. Since Dav Whatmore had taken over as coach, they had put up a decent showing in Australia and run Pakistan incredibly close in a Test in Multan, and consequently it was England who were dogged by the fear of failure. The first Test at Dhaka was a case in point - by the close of the fourth day, Bangladesh were 153 runs ahead with five wickets standing, and a major upset could not be entirely ruled out. But Steve Harmison and Matthew Hoggard shared 16 wickets in the match to ensure that England ultimately avoided embarrassment, and it was midway through the second Test at Chittagong that Bangladesh's resolve snapped. A 2-0 series win looked comfortable enough on paper, but it was not achieved without some anxious moments.
Tests: Bangladesh 0 England 2
ODIs: Bangladesh 0 England 3

2005 (England)
Bangladesh never had a chance of competing in an early-season series where conditions were completely alien to the them. They were duly blown away by an innings in both Tests - with each barely stretching into the third day - as England warmed up for the Ashes contest that started a few months later. At Lord's England's quicks shared the wickets - Gareth Batty didn't even get a bowl - while Marcus Trescothick and Michael Vaughan helped themselves to hundreds. Chester-le-Street was equally one-sided as Steve Harmison's 5 for 32 blew Bangladesh away for 104 before England replied with 447 for 3 at nearly six-an-over. There was another hundred for Trescothick and a first for Ian Bell as he plundered 162. Graham Thorpe, in his 100th Test, hit an unbeaten 66 and it proved to be his final international innings - he was replaced by Kevin Pietersen against Australia. Bangladesh at least managed 316 second time around, but their greatest moment of the tour came a few weeks later when they famously beat Australia in the Natwest Series at Cardiff.
Tests England 2 Bangladesh 0

2009-10 (Bangladesh)
Another clean-sweep for England, but for the first time they were really made to work for their rewards, as a combination of gritty opponents and deathly-flat tracks ensured that both Tests were carried into the final day. England were led for the first time by Alastair Cook, who took the reins when Andrew Strauss was given permission to miss the tour by the ECB, and though his leadership in the field lacked a touch of authority, he was in fine touch with the bat with hundreds in each Test, including a hefty 173 at Chittagong. Thanks to Junaid Siddique, who produced his maiden Test century in the second innings, England were held up in their pursuit of victory before Graeme Swann wrapped up the match with a career-best 10-wicket haul, an effort that carried him to No. 2 in the world. At Dhaka, Tamim Iqbal thrilled his home fans with a blistering first-morning 85 from 71 balls, a performance that would surely have carried him to a rare century before lunch had he not fallen to a dubious caught-behind decision. Tamim had also shone in the preceding ODI series, with a century in the first match, before Eoin Morgan rescued England from an embarrassing defeat in the second game, scoring 110 not out in a two-wicket win.
Tests England 2 Bangladesh 0
ODIs England 3 Bangladesh 0