Al Qa'eda have been attacking the US for years (the first WTC bombing in ?1993, and the bombings at US Embassies in Nairobi and Dar es Salaam). The UK didn't seem to feature on their radar (not enough to attack us, at least), until our staunch and unilateral (virtually) support for Dubya's invasion of Iraq which seemed to change all that...strange really...
Al Qaeda springs from the "Muslim Brotherhood" movement that began as an opposition to Nasser's corrupt, secular Egyptian government. The movement was strengthened by Egypt's signing of a peace treaty with Israel - an event that led directly to the assassination of President Assad by the Brotherhood. The movement also gained a foothold in Saudi Arabia amongst Islamic opponents of the corrupt and avowedly pro-western Saudi government. Al Qaeda and The Muslim Brotherhood's anti-western stand is based upon the creation of and continuing support for the state of Israel and the west's support of the Saudi regime.
The first Gulf War and the use of Saudi Arabia as a base for US led forces inflamed the Saudi extremists in particular, with Al Qaeda rising to leadership of "the cause" and leading directly to the attacks upon the World Trade Centre. The fight against the Taliban and the invasion of Iraq are not the cause of terrorism - although they do contribute to terrorist propaganda - but pulling out of Iraq and Afghanistan would do nothing to end terrorism, because the original root causes remain.