Metal–organic frameworks (MOFs) containing ZrIV‐based secondary building units (SBUs), as in the UiO‐66 series, are receiving widespread research interest due to their enhanced chemical and mechanical stabilities. We report the synthesis and extensive characterisation, as both bulk microcrystalline and single crystal forms, of extended UiO‐66 (Zr and Hf) series MOFs containing integral unsaturated alkene, alkyne and butadiyne units, which serve as reactive sites for postsynthetic modification (PSM) by halogenation. The water stability of a Zr–stilbene MOF allows the dual insertion of both −OH and −Br groups in a single, aqueous bromohydrination step. Quantitative bromination of alkyne‐ and butadiyne‐containing MOFs is demonstrated to be stereoselective, as a consequence of the linker geometry when bound in the MOFs, while the inherent change in hybridisation and geometry of integral linker atoms is facilitated by the high mechanical stabilities of the MOFs, allowing bromination to be characterised in a single‐crystal to single‐crystal (SCSC) manner. The facile addition of bromine across the unsaturated C−C bonds in the MOFs in solution is extended to irreversible iodine sequestration in the vapour phase. A large‐pore interpenetrated Zr MOF demonstrates an I2 storage capacity of 279 % w/w, through a combination of chemisorption and physisorption, which is comparable to the highest reported capacities of benchmark iodine storage materials for radioactive I2 sequestration. We expect this facile PSM process to not only allow trapping of toxic vapours, but also modulate the mechanical properties of the MOFs.