Not withstanding the info above, I think it may have been quite simple.
After the end of the official warfighting phase of OIF and then the start of the insurgency, the British sincerely believed that they were on top of the COIN campaign due to their decades of experience in Northern Ireland and previous success in Malaya and Kenya. What they didn't pick up on and which took some years for the penny to drop is that COIN truisms don't translate easily between environment and that the UK approach of treating the Iraqi insurgency as they would one in a Commonwealth or Western-oriented nation was doomed from the start.
To make matters worse, a number of Brits, mainly at quite senior levels, felt that they had some form of almost God-given superiority over the US (small nation syndrome) and this attitude was probably a major factor in the long period it took the UK to realise they had gotten it wrong and adapting accordingly - had the attitude being more of learning from others had been, perhaps the case for more troops earlier could have successfully been made?
Nowhere have I heard it summed up better than senior UK officer last year "...really..instead of sniping at the Americans from the sidelines of our own superiority, we should have been following them around with our notebooks open, furiously taking notes..."
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