Answer by taking a quote from the following article:

Kwame Nkrumah PC (21 September 1909 - 27 April 1972) was a Ghanaian politician and revolutionary. He was the first prime minister and president of Ghana, having led it to independence from Britain in 1957. An influential advocate of Pan-Africanism, Nkrumah was a founding member of the Organization of African Unity and winner of the Lenin Peace Prize in 1962. After twelve years abroad pursuing higher education, developing his political philosophy, and organizing with other diasporic pan-Africanists, Nkrumah returned to Gold Coast to begin his political career as an advocate of national independence.

Nkrumah returned to London in May 1945 and enrolled at the London School of Economics as a PhD candidate in anthropology. He withdrew after one term and the next year enrolled at University College, with the intent to write a philosophy dissertation on "Knowledge and Logical Positivism". His supervisor, A. J. Ayer, declined to rate Nkrumah as a "first-class philosopher", saying, "I liked him and enjoyed talking to him but he did not seem to me to have an analytical mind. He wanted answers too quickly. I think part of the trouble may have been that he wasn't concentrating very hard on his thesis. It was a way of marking time until the opportunity came for him to return to Ghana." Finally, Nkrumah enrolled in, but did not complete, a study in law at Gray's Inn. Nkrumah spent his time on political organising. He and Padmore were among the principal organizers, and co-treasurers, of the Fifth Pan-African Congress in Manchester (15-19 October 1945). The Congress elaborated a strategy for supplanting colonialism with African socialism. They agreed to pursue a federal United States of Africa, with interlocking regional organizations, governing through separate states of limited sovereignty. They planned to pursue a new African culture without tribalism, democratic within a socialist or communist system, synthesizing traditional aspects with modern thinking, and for this to be achieved by nonviolent means if possible. Among those who attended the congress was the venerable W. E. B. Dubois along with some who later took leading roles in leading their nations to independence, including Hastings Banda of Nyasaland (which became Malawi), Jomo Kenyatta of Kenya, Obafemi Awolowo of Nigeria, and C. L. R. James. The congress sought to establish ongoing African activism in Britain in conjunction with the West African National Secretariat (WANS) to work towards the decolonization of Africa. Nkrumah became the secretary of WANS. In addition to seeking to organise Africans to gain their nations' freedom, Nkrumah sought to succor the many West African seamen who had been stranded, destitute, in London at the end of the war, and established a Coloured Workers Association to empower and succor them. The U.S. State Department and MI5 watched Nkrumah and the WANS, focusing on their links with Communism. Nkrumah and Padmore established a group called The Circle to lead the way to West African independence and unity; the group aimed to create a Union of African Socialist Republics. A document from The Circle, setting forth that goal, was found on Nkrumah upon his arrest in Accra in 1948, and was used against him by the British authorities.

What happened after he got there?
enrolled at the London School of Economics as a PhD candidate in anthropology.