Increasing attention has been devoted to the design of layered double hydroxide (LDH)-based hybrid materials. In this work, we demonstrate the intercalation by anion exchange process of poly(acrylic acid) (PAA) and three different hydrophilic random copolymers of acrylic acid (AA) and n-butyl acrylate (BA) with molar masses ranging from 2000 to 4200 g mol$^{−1}$ synthesized by reversible addition-fragmentation chain transfer (RAFT) polymerization, into LDH containing magnesium(II) and aluminium(III) intralayer cations and nitrates as counterions (MgAl-NO$_3$ LDH). At basic pH, the copolymer chains (macroRAFT agents) carry negative charges which allowed the establishment of electrostatic interactions with the LDH interlayer and their intercalation. The resulting hybrid macroRAFT/LDH materials displayed an expanded interlamellar domain compared to pristine MgAl-NO$_3$ LDH from 1.36 nm to 2.33 nm. Depending on the nature of the units involved into the macroRAFT copolymer (only AA or AA and BA), the intercalation led to monolayer or bilayer arrangements within the interlayer space. The macroRAFT intercalation and the molecular structure of the hybrid phases were further characterized by Fourier transform infrared (FTIR) and solid-state $^{13}$C, $^1$H and $^{27}$Al nuclear magnetic resonance (NMR) spectroscopies to get a better description of the local structure.