The Spanish and Moroccan governments are talking about building
a high-speed rail tunnel under the Strait of Gibraltar, linking Europe and Africa. If it happens (and that is a big if; the entire endeavour would cost about US$13 billion and cost 20 years to construct), it would make it possible to travel from one continent to another by rail.
How far down through Africa railways could extend is another matter; I imagine a London-Johannesburg rail link would be pushing it.