It is not particularly accurate to say this. It is true that business interests were in favor of taking more of Africa. However, most Britons would have agreed that taking more of Africa was in the national interest.
The Scramble for Africa was caused in part by the fact that European businesses needed raw materials and new markets. In this sense, the Scramble can be attributed to the needs of elite businessmen.
However, this was by no means the only motivation for the Scramble. Britain and other imperial countries truly believed that taking empires in Africa was in their national interests. They were very much concerned with maintaining their status as major world powers. They felt that the possession of large empires was important for this.
The Scramble for Africa was not caused by elite businessmen manipulating their governments. Instead, it was caused by governments feeling that African empires were needed for economic reasons, but also for military and strategic reasons and reasons of prestige.