pH-Responsive microgel particles are crosslinked polymer colloid particles that swell when the pH approaches the pK a. They have attracted a great deal of interest because of the ability to prepare stimulus responsive dispersions. Microgels that have only one form of crosslinking are termed singly crosslinked microgels (SX microgels). SX microgels are defined here as microgel particles that contain intra-particle linkages as the only source of covalent crosslinks. Recently, we introduced the first examples of a new family of pH-responsive doubly crosslinked microgel (DX microgels) [Liu et al., Soft Matter, 2011, 7, 4696]. DX microgels are hydrogels composed of covalently-linked functionalised SX microgel particles. DX microgels contain inter-particle crosslinking as well as intra-particle crosslinking. Here, we investigate pH-responsive DX microgels prepared using a new, more versatile, microgel functionalisation strategy. Carbodiimide chemistry is used to vinyl-functionalise poly(MMA/MAA/EGDMA) (methyl methacrylate, methacrylic acid and ethyleneglycol dimethacrylate) microgels (abbreviated as M-EGD). The DX microgels were prepared using pH-triggered inter-penetration of 2-aminoethylmethacrylate (AEM) functionalised SX microgels and free-radical crosslinking. The DX microgels based on M-EGD had built-in microporosity. Furthermore, dynamic rheology data show for the first time that the elastic modulus of DX microgels is proportional to the extent of vinyl group functionalisation. The generality of this approach was demonstrated by the preparation of DX microgels based on poly(EA/MAA/BDD) (ethylacrylate and 1, 4-butanediol diacrylate), which is abbreviated as E-BDD. The pH-responsive DX microgels have high elastic modulus values, swell strongly and have low sol fractions. They are injectable and the DX microgels have improved swelling at low pH which should increase the pH range for potential biomaterial applications. The data are compared with those reported by Liu et al. and the differences discussed. © 2011 The Royal Society of Chemistry.