Polymer brushes are assemblies of polymer chains grafted with one end group to a solid surface in a number high enough so that the chains are stretched away from the interface due to steric hindrance and/or electrostatic repulsion between neighbouring polymer units. Diblock copolymers have been used to build controlled switchable surfaces with a selective response to external stimuli specific to one of the blocks. Herein we study the structure, mechanical behaviour and interfacial softness of a diblock copolymer brush composed of N,N′-dimethylmethylacrylamide (DMMAA) and methacrylic acid (MAA) considering different counterions and Hofmeister salts by means of atomistic molecular dynamics simulations. Li⁺, Na⁺, K⁺, Rb⁺ and Cs⁺ were used as counterions while NaF, NaCl, NaBr and NaI 1 molal aqueous salt solutions were used to study anion effects. Our results show that Li⁺ and Na⁺ cations form a strong salt bridge network with the carboxylic groups of MAA monomers belonging to neighbouring chains leading to a stretched monodisperse arrangement of the polymeric chains. On the other hand, the weaker salt bridge network upon addition of Rb⁺ and Cs⁺ cations promotes a partial collapse of the polyelectrolyte brushes. Addition of K⁺ cations leads to an intermediate arrangement. These results have a direct impact on the mechanical behaviour of such soft surfaces and the packing of the polymer chains, i.e. the rigidity of the brush is ion specific and follows a Hofmeister series in the order Li⁺ > Na⁺ ≫ K⁺ > Rb⁺ > Cs⁺. We furthermore report that in those systems where a sodium halide salt is added, the same swelling behaviour is observed independently of the nature of the added salt. However, the degree of ionic absorption within the brush is again ion specific in the order NaCl > NaBr > NaI > NaF at 1 m salt concentration.