In the case of suicide attacks, there is a reasonable argument to be made that they are “un-Islamic” in view of the fact that classically Islam had a strong prohibition against suicide, which was weakened in the context of attacks on non-Muslims only since the 1950’s under the influence of the writings of Saayed Qutb.
This case, however, should be made by Muslim ulema, not non-Muslims (taking a position on what is or is not consonant with a religion of which one is not an adherent of is rather absurd: one really does not expect a Muslim, Buddhist, Jew or atheist to have a valid position on a matter of controversy among Christians, like, say, the “Rapture” or the papal claims). Alas, they are remarkably unwilling to do so — I believe only one imam based in London has issued a blanket condemnation of “martyrdom operations”, all other condemnations made publicly have carved out exceptions for Muslim lands under non-Muslim occupation (meaning primarily Israel, though the argument given would apply to Afghanistan, and potentially any Muslim nation hosting military bases for non-Muslim nations) or attacks on non-Muslim nations occupying or fighting against Muslims in their own lands (making the condemnation nearly meaningless).
However, it is very hard to argue that attacks by Muslims on non-Muslims which, like the murder of Lee Rigby, follow explicitly the Qu’ranic edict “strike at the necks of the unbelievers” in which the attacker explicitly cites Islam as his motivation are not directly rooted in Islam. (Though if Baroness Warsi wants to try, I’ll be interested to hear her argument and compare it with the positions of noted ulema both Sunni and Shia.)
bfl