Not in Iraq, but in Northern Ireland, that is. As the BBC reports:
The British army's operation in Northern Ireland came to an end at midnight on Tuesday after 38 years.That's some seriously good news. I don't for a moment believe that Northern Ireland isn't going to hit rough patches in the future, but a British Army pullout would have been considered a pipe dream not too many years ago.
Operation Banner - the Army's support role for the police - had been its longest continuous campaign, with more than 300,000 personnel taking part.
A garrison of 5,000 troops will remain but security will be entirely the responsibility of the police.
British troops were sent to Northern Ireland in 1969 after violent clashes between Catholics and Protestants.
When the first soldiers were deployed in August 1969, commanders believed they would be in Northern Ireland for just a few weeks.
But the Army quickly became involved in what came to be known as Operation Banner.
The British Army end strength in Northern Ireland peaked at 27,000 troops. I don't have a date when that peak occurred, nor do I know the date at which the Royal Ulster Constabulary (the police force during the Troubles) end strength peaked at 8500 plus 5000 reservists, nor do I know the population of Ulster at that time. But, figuring that the population was somewhere around 1.4 to 1.6 million , and guesstimating that the RUC and RA forces peaked around the same time, the "troop density" in Northern Ireland maxed out at around 22 counterinsurgents per thousand population. All this is relevant to the current mess in Iraq, because according to the US Army's Counterinsurgency manual , paragraph 1-67:
However, no predetermined, fixed ratio of friendly troops to enemy combatants ensures success in COIN. The conditions of the operational environment and the approaches insurgents use vary too widely. A better force requirement gauge is troop density, the ratio of security forces (including the host nation's military and police forces as well as foreign counterinsurgents) to inhabitants. Most density recommendations fall within a range of 20 to 25 counterinsurgents for every 1000 residents in an AO. Twenty counterinsurgents per 1000 residents is often considered the minimum troop density required for effective COIN operations; however as with any fixed ratio, such calculations remain very dependent upon the situation.Even with the much-vaunted "surge", the US troop density (160,000 total) in Iraq falls way short of the twenty-per-thousand that GEN Petraeus called for in FM 3-24. If you add in the Iraqi army and national police (whose end-strength "officially" is 353,100 ), the resulting total of 513,000 is almost enough to reach the twenty-per-thousand mark for the IRaqi population of 27 million  - we'd need 540,000 to accomplish that. And that's assuming that all the Iraqi Security Forces actually show up - I can't find the link off hand, but I do recall reading that if only half of an Iraqi unit fails to report for duty, it's considered a good sign by the Iraqi commanders.
but let's assume that there really are enough boots on the ground, at the moment, for effective counterinsurgency. The British Army spent thirty eight years on Operation Banner, with the support of at least half the local population. It took nearly four decades of fighting and politicking to get to the point where the Army no longer needs to support the local police service. Is there anybody in the United States who truly believes the American public is willing to spend the next four decades in the middle of the Iraqi Civil War?
 According to Wikipedia at http://en.wikipedia.org/wiki/Royal_Ulster_Constabulary
 The 2001 population was 1,685,267 in 2001, according to the census, so this is a decent guess.
 FM 3-24; also known as MCWP 3-33.5 to the Marines.
 According to the State Department's "Iraq Weekly Status Report" dated June 20, 2007 at http://www.state.gov/documents/organization/87080.pdf
 Per the CIA World Factbook at https://www.cia.gov/library/publications/the-world-factbook/geos/iz.html#People
[Edited to correct incorrect references to the "Royal" Army]