Experimental studies have reported the possibility of affecting the growth/dissolution of amyloid fibres by the addition of organic salts of the room-temperature ionic-liquid family, raising the tantalizing prospect of controlling these processes under physiological conditions. The effect of [Tea][Ms] and [Tea][H₂PO₄] at various concentrations on the structure and stability of a simple model of Aβ42 fibrils has been investigated by computational means. Free energy computations show that both [Tea][Ms] and [Tea][H₂PO₄] decrease the stability of fibrils with respect to isolated peptides in solution, and the effect is significantly stronger for [Tea][Ms]. The secondary structure of fibrils is not much affected, but single peptides in solution show a marked decrease in their β-strand character and an increase in α-propensity, again especially for [Tea][Ms]. These observations, consistent with the experimental picture, can be traced to two primary effects,i.e., the difference in the ionicity of the [Tea][Ms] and [Tea][H₂PO₄] water solutions and the remarkable affinity of peptides for [Ms]⁻ anions, due to the multiplicity of H-bonds.