Writing in Foreign Policy, Alex de Waal is certain that Brexit is terrible for African countries, and that “[e]verything from the economy to peacekeeping missions will suffer.”

The damage to British interests is significant, but the losses for [African countries] could be greater still. In campaigning to leave the European Union, Minister for Africa James Duddridge argued that Britain would be able to forge stronger ties with the continent if it were unencumbered by EU inefficiencies in aid and trade. Perhaps if Duddridge had a blank slate on which to construct a new Africa policy, he could do better than Britain’s existing one, which is part bilateral and part multilateral through the EU. But no policy is ever built on a blank slate, and surveying the post-Brexit political wreckage, he is now faced with a salvage job that will involve decoupling Britain from numerous EU-led peace and development initiatives and renegotiating dozens of trade deals. Even deftly managed by Duddridge or his successor, the Brexit will leave Britain with a fraction of the influence it currently wields in Africa.

And over at Africa is a Country Grive Chelwa notes that:

The one obvious channel through which Brexit could affect economies in Africa is if it triggers a recession in the UK. A recession might affect trade and investment between the two regions. The Bank of England thinks a recession might very well be on the cards. A study reviewing all studies that have estimated the likely economic impact of Brexit found: “GDP losses for the UK in the range of 10% or more [could not] be ruled out in the long run.”

How much trade takes place between the UK and Africa? Not much, it turns out. Combining data from the UK’s Office for National Statistics (ONS) and the United Nations Conference on Trade and Development (UNCTAD) for 2014, the latest year for which we have comparable data, we calculated that exports from Africa to the UK represent about 5% of Africa’s total exports. Africa is more worried about a slowdown in China, its biggest trading partner by far.

…. The UK doesn’t have the same influence on the continent that it did decades ago. And Brexit will be further proof of that. If the UK sneezes Africa will … well Africa will say “bless you” and move on.

On balance, I agree with Chelwa. It appears that with regard to the UK-Africa relationship, the Brits stand to lose more than Africa as a unit following Brexit. This is for the following reasons:

1. Lacking the amplifying effects of the EU, UK influence in Africa will be diminished. This is bad for the UK, but not necessarily so for African states. Notice that the UK’s security objectives in Somalia or elsewhere on the Continent have not suddenly changed following the Brexit vote. We should disabuse ourselves of the notion that the UK involvement in these theatres of conflict is out of pure benevolence. It is largely to protect British interests (tourists, MNCs, aid workers, other tied aid, etc). Those interests have not suddenly changed with Brexit. Is a post-Brexit UK better off with a stable Somalia? I think so. Viewed this way, what Brexit has done is not to change British interests in Africa but to increase the UK’s transaction costs in catering to those interests. The Brits may invest less in specific peacekeeping operations, but their self-interest dictates that they will not suddenly close the taps on these investments.
2. A diminished UK diminishes Europe, which may reduce Europe’s leverage vis-a-vis African countries. This outcome could cut both ways. On the one hand, it may exacerbate the moral hazard problem faced by African leaders by allowing them to play different European powers off each other (why invest in good governance if Europe is always at the ready to help if things go south?) But on the other hand, a weaker Europe may be less willing to bail out African leaders all the time. This might force these leaders to take their jobs seriously, thereby improving the welfare of their citizens. 
3. It is not clear that decoupling UK aid from the rest of Europe will necessarily lead to the UK cutting its aid budget. In fact, the opposite might prove true. Going its own way may force the UK to put more aid pounds into projects in the region than it currently does under a joint EU aid budget. Again, increased transaction costs may mean the UK spending more money than it currently does in Africa, which is good for African economies. Plus the UK is likely to find itself needing to make up for the lost amplifying effects of the EU with more aid pounds.
4. A recession in the UK may prove contagious. This would be bad for the world economy, and Africa would not be an exception. That said, I don’t think economic turbulence in Africa would necessarily lead to the conflicts of the early 1990s. With a few glaring exceptions, most African countries would be able to withstand a global recession without collapsing. We saw this during the Great Recession.
5. The world is learning a lot about democracy by observing the challenges it currently faces in the West. Suddenly, corrosive ethnic politics is not exclusive to poor countries. “Leaders” like Donald J. Trump and Boris Johnson are not things that only happen in Zimbabwe or Nicaragua. These data points will serve to demystify democracy as a system of governance, and refocus global attention on what really makes democracy work — a stable intra-elite consensus coupled with reasonably sufficient responsiveness to the electorate (down with the fetishization of elections!!!) This will be a valuable lesson for Africa and other developing regions of the world. The ongoing sociopolitical troubles in the West are bound to liberate the worldview of leaders and other elites in the Global South, and will empower them to mold their own societies in their own image, instead of trying to turn them into Denmarks. The often-misrepresented “European mystique” has lost its shine. And this is a good thing for the world.

This is not to say that Africa’s economies will be able to weather Brexit without any non-trivial hiccups. South Africa, Nigeria, and Kenya are probably the most exposed (in that order). Other African economies will be exposed to the extent that economic troubles in the UK lead to a global recession (the gold exporters might even benefit…)

And Western security policies and support for missions in Somalia and across the Sahel may face short-term uncertainties. But these experiences will not necessarily be catastrophic (on the security front, America will most likely steady the ship).

In fact, I tend to think that the long-run impact of these experiences will be positive. English speaking African economies will have incentives to diversify their export destinations away from the UK. African countries will have more leverage vis-a-vis the UK and (a fractured) Europe (and the US). And the lessons from the political upheavals in the West will serve to liberate Global South elites to mold their own societies in their own image and in a manner that respects sociopolitical realities in their specific contexts.