The Reversible Addition-Fragmentation chain-Transfer (RAFT) synthesis of poly(glycidyl methacrylate) (PGMA) copolymers followed by the post-polymerisation treatment with morpholine allows the rational design of amphiphilic block copolymers that are capable of efficiently dispersing single walled carbon nanotubes (SWCNTs) in aqueous media, as shown by comparative photophysical characterisation and AFM analysis.