There he won the "Profumo Prize" for being the best scholar in law, following his performance in the university's final bar (LLB) examination.

He, together with Dr J.B. Danquah, played a prominent role in achieving the joint Ashanti Colony Collaboration which resulted in the 1946 Burns Constitution.

After Ghana's independence in 1957 he was appointed the first High Commissioner to the United Kingdom with concurrent accreditation to France by dr. Kwame Nkrumah.

Events that highlighted his tenure in that office include the assault on him that made international headlines of which much scholarly work have been done on; in January 1959, Patrice Lumumba, the prime minister of the Democratic Republic of the Congo, stayed at The Ritz Hotel, London and met with Adjaye and others in the restaurant.

In 1962 he was a member of a three-man (which included Sir Henry Wynn Parry and Justice Gopal Das Khosla of India) committee known as the Wynn-Parry Commission of Inquiry set up on 11 May 1962 to investigate the causes of the political disturbances in Guyana which took place on February 16, 1962, popularly known in Guyanese history as "Black Friday".

Hugh Foot of the UK, appointed by the UN secretary General U Thant to examine the explosive problem of South Africa’s racial policies in accordance with UN Security Council Resolution of 4 December 1963.