Most historians today would say that empire was generally not a direct source of surplus revenue to the British state during the period you are interested in, despite ongoing efforts to make imperial holdings be self-sufficient. This is less due to the costs of investments in infrastructure such as railroads (which were limited, and often constructed in significant part with unpaid forced labor), and more due to the costs of paying bureaucrats, soldiers, and police. I would also not attribute the costs of the British navy to empire per se, but rather to the connected-but-separate issue of the British attempt to enforce 'free trade' policies that allowed British merchants access to market in both British and non-British overseas spaces.

There are also arguments for the advantages of empire. Some private corporations found it exceedingly profitable; the Royal Niger Company, which was eventually incorporated into Lever Bros., is a case in point. During wartime, empire also provided sources for both manpower and crucial natural resources.

It's worth noting here that Germany did have a reasonably significant African empire until WWI, including Tanzania, Cameroon, and Namibia. The more relevant contrast might be with the United States. Despite the current move to rethink American history through an imperial lens, it's certainly true that the US tended to prefer the mechanisms of informal empire (discounting here the conquest of the areas that eventually became fully incorporated in the US), with associated cost savings.