There were a few Islamic polities in Africa that managed to fend off colonialism for longer than other parts of Africa (e.g. Wadai, the Dervish State). How big a factor was Islam in anticolonialism, and is there a relationship between this and today’s militant groups eg Boko Haram and al-Shabaab?

Yes, you can point to several Islamic polities that put up a prolonged resistance to European imperialism, like the Dervish state, Samori Toure's Wassolou emirate, and prolonged Senussi resistance to Italian rule in the Fezzan and in Wadai.

On the other hand, the sultan of Zanzibar fought a famously brief war (38 minutes) against the British.

The Swahili adventurer Tippu Tip operated in the eastern Congo and created a quasi-state, on territory that the Congo Free State also claimed. At first his forces fought Force Publique soldiers, but by 1887 Tippu Tip had seemingly opted for a path of accommodation, and had managed to get himself appointed as a regional governor of the Congo Free State. But after his retirement, conflicts arose again and the Swahili-Arab merchants/slave traders were again at war with Force Publique between 1892-1894.

Similarly, the Emirs of the Sokoto caliphate were incorporated into the British colony of Northern Nigeria as local administrators, following a British policy of "indirect rule".

Or consider that the Mahdist state in the upper Nile valley, what is now Sudan, began as a revolt against the excesses of a Turco-Egyptian imperial project by Muhammad Ali Pasha and his descendants.

So, I don't believe that there is something inherent to Islam that required adherents to resist European rule to a greater extent than non-muslim societies did. At the same time, we must acknowledge that Islam is not and was not a monolith, but that it contains many different schools of thought that contend with each other.

For example, I mentioned above the Senussi Sufi religious order, which fought French and Italian efforts to control the Fezzan region of Libya through force of arms.

On the other hand, Ahmadu Bamba and the Muridiyya Sufi school laid out an ideology of spiritual renewal and deeper understanding of faith. Although in many ways Bamba and his successors followed a political policy of accommodation towards French governance, French administrators feared that his message of spiritual renewal could lead towards armed jihad against French rule (something Bamba and his successors always denied). To limit this threat, French administrators twice exiled him, to Gabon from 1895-1902 and after a short return, to Mauritania from 1903-1907.

However, these exiles gave rise to many popular myths about Ahmadu Bamba's spiritual strength, and ability to resist torture, deprivation, and persecution by the French. These popular stories only enhanced the popularity of the Murid religious order.

By 1910, French authorities had changed their minds about Bamba's intentions, and no longer sought to suppress him and his order. For the last 17 years of his life, the Muridiyya order and Colonial authorities came to greater degrees of accommodation with each other. During the First World War, Bamba encouraged enlistment in colonial regiments of the French army. On the other hand, the popularity of the order meant that local political officials sought Muridiyya endorsement, and the order thus became an important power-broker in Senegalese and Mauritanian local politics in the colonial era, and the Muridiyya continue to be extremely influential in Senegalese politics today.

So, the clearest way to say it would be that Muslim scholars who were anti-colonialist or anti-imperialist, saw in Islam messages that could be used to justify armed or unarmed resistance, or else used to justify accommodation with European rule.

Thus, I would be very careful about drawing a connection between the ideology of Boko Haram or al-Shabaab and "Islamic anti-colonial thought", because there was not one single Islamic response to colonialism.

I think also, you can not understand Boko Haram or al-Shabaab or Al Qaeda without paying attention to the political-intellectual trends within Islam since the 1960s (i.e. in the post-colonial era), which have been influenced by the writings of Said Qutb and others of the Egyptian Muslim brotherhood, as well as Saudi influence through the promotion of Wahhabist understandings of Islam. I'm going to mention /u/Cpt_Buck here, because I think he is more versed in modern Islamic/Islamist politics than I am.

Now, it would be fair to say that Qutb and the Egyptian Muslim Brotherhood, and Saudi Wahhabism, represent specific intellectual responses to Colonialism. However, maybe not responses that originated in sub-Saharan Africa, and not the only responses. The neighbors/victims of Boko Haram and al-Shabaab are also muslims and are also the inheritors of the engagement with colonialism.