Why did the U.S and Britain invade Afghanistan in 2001?

There are several clarifications that need to be made to
your question.

1.  The U.S. and England were not the only
countries to send troops to Afghanistan in 2001/2002--to this day, there are many NATO
countries with troops in the region.

2.  The U.S. did not
attack Afghanistan.  It attacked Al Qaeda--a global terrorist organization which had its
base in Afghanistan at the time--and the Taliban, the radical ruling group of the
country which oppressed its own people and willingly gave shelter to Osama bin Laden and
Al Qaeda.

3.  In 2001, the United States and England began
working with many native Afghans to rid their country of terrorists and to place the
decision-making process back in the hands of the Afghan people not in the hands of an
elite few who terrorized their own countrymen.  Many of the Afghans who assisted and who
still assist U.S. forces were followers of Massoud (an Afghan leader who fought against
the Taliban until he was assassinated two days before 9/11), and they would not see the
U.S. and England as attacking their country.