Thin films of poly(methyl methacrylate) and poly(vinyl chloride) of different thickness are used to investigate the effect of spatial confinement on the efficiency of bond breaking induced by 2 MeV H^{+} and 2.1 GeV Bi ions. Effective cross sections for oxygen and chlorine loss are extracted for films down to a thickness of about 5 nm and are compared to theoretical estimations based on radial energy density profiles simulated with geant-dna. The cross sections are to a large extent thickness independent, indicating that bond breaking is dominated by short-range processes. This is in contrast to the strongly reduced efficiencies found recently for cratering induced by high-energy ions in similar ultrathin polymer films [Phys. Rev. Lett. 114, 118302 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.118302].