We consider the generalised Krein-Feller operator $Δ_{ν, μ} $ with respect to compactly supported Borel probability measures $μ$ and $ν$ with the natural restrictions that $μ$ is atomless, the supp$(ν)\subseteq$supp$(μ)$ and the atoms of $ν$ are embedded in the supp$(μ)$. We show that the solutions of the eigenvalue problem for $Δ_{ν, μ} $ can be transferred to the corresponding problem for the classical Krein-Feller operator $Δ_{ν\circ F_μ^{-1}, Λ}$ with respect to the Lebesgue measure $Λ$ via an isometric isomorphism determined by the distribution function $F_μ$ of $μ$. In this way, we obtain a new characterisation of the upper spectral dimension and consolidate many known results on the spectral asymptotics of Krein-Feller operators. We also recover known properties of and connections to generalised gap diffusions associated to these operators.