The British annexed Lagos in:

The British annexation of Lagos took place in 1861. This event followed a period of increasing British involvement in Lagos affairs, driven largely by the desire to suppress the slave trade and protect British commercial interests along the West African coast.

In 1851, the British had already intervened militarily in Lagos, deposing the pro-slave-trade ruler Oba Kosoko and installing the more cooperative Oba Akitoye. However, this did not amount to formal annexation. Akitoye's successor, Oba Docemo, found himself under growing British pressure, and on 6 August 1861, he signed a treaty ceding Lagos to the British Crown. Lagos then became a British colony, administered initially as part of the settlements along the West African coast.

The annexation of Lagos was significant because it marked the beginning of direct British colonial rule in what would eventually become Nigeria. Lagos served as the administrative base from which British influence expanded into the interior throughout the rest of the 19th century.

The other dates offered do not correspond to this event. 1841 predates significant British intervention in Lagos, while 1871 and 1881 fall after the annexation had already occurred.