Michael Barnett in his 2005 essay “The many faces of Rasta: Doctrinal Diversity within the Rastafari Movement” gives description of main branches of Rastafari: Twelve tribes of Israel, BoboShante and Nyabinghi Order.
First part of the chapter on Nyabinghi Order also goes into the origins of Rastafari dreadlocks:

The Nyahbinghi Order

This Mansion is the oldest of the previously mentioned in that it has its roots strongly connected to those of the vintage Rastafari.

The Nyahbinghi order is generally regarded as the most orthodox mansion within the broader Rasta movement and is variously known as the House of Nyabinghi, Theocracy Reign Ancient Order of Nyahbinghi, the Theocratic Government of Rastafari, Haile Selassie I, and even the Theocratic assembly.

The term Nyahbinghi according to Campbell came from the anti -colonialist movement of Kigezi in Uganda which called for death to Black and white oppressors.

The University of the West Indies Report, details that on the 7th December 1935 the Jamaica Times published an account of the Nyahbinghi Order in Ethiopia and the Congo.
According to this account in the Times, the Ethiopian Emperor was head of the Nyahbinghi Order, the purpose of which was to overthrow the white (Italian) domination of Ethiopia, by racial war.

According to the University Report the term Nyahbingi came to mean in Jamaica, for many Rastafari, death to Black and white oppressors.
Those who were in accord with this ideology quickly adopted the title, Nyah-men (alternatively spelt as Niyamen).

What is clear from the University Report is that Leonard Howell’s followers at Pinnacle were perceived by the researchers to be the most prone to violence of all the Rastas in Jamaica; they further argue that from 1933 Howell had been preaching violence, thus they surmise that it was mainly Howell’s followers who adopted the name, Nyahmen, and who appropriated a countenance that was consistent with the name.

Howell’s followers are also credited by the University Report to have been the first dreadlocked Rastamen (locksmen) in the history of the
movement, appearing on the scene with the second installation of the Pinnacle camp in 1943.
However, according to Chevannes , the first dreadlocked Rastamen were those of the Youth Black Faith movement, who took on this appearance in about 1 947. In weighing both accounts this researcher proposes that there is validity in both, on the basis that it is highly possible that both the Youth Black faith Movement and the Howellites were inspired by the Mau Mau who spearheaded the revolt against the British colonial powers in Kenya.
This perspective takes into account that much of the early history of Rastafari is derived from oral testimonies and is thus subject to distortion, as Chevannes so astutely points out.


However, while Ras Boanerges (Bongo Wato), one of the founders of the Youth Black Faith has given testimony that his organization was the first to start wearing dreadlocks, this writer feels that there are too many accounts of Howellites who used to stand guard over the second installation of the pinnacle camp, having dreadlocks, to be discounted.
What we do know is that by the early 1950s the wearing of dreadlocks starts to become visible among the Jamaican Rastafarian community and this very noticeably coincides with the prominence of
the Mau Mau in Kenya.

Was this merely a coincidence?
…

From:

The many faces of Rasta: Doctrinal Diversity within the Rastafari Movement
By: Michael Barnett
Source: Caribbean Quarterly, Vol. 51, No. 2 (June 2005)