Radiation protection dosimetry in radiation fields behind the shielding of high-energy accelerators such as CERN is a challenging task and the quantitative understanding of the detector response used for dosimetry is essential. Measurements with ionisation chambers are a standard method to determine absorbed dose (in the detector material). For applications in mixed radiation fields, ionisation chambers are often also calibrated in terms of ambient dose equivalent at conventional reference radiation fields. The response of a given ionisation chamber to the various particle types of a complex high-energy radiation field in terms of ambient dose equivalent depends of course on the materials used for the construction and the chamber gas used. This paper will present results of computational studies simulating the exposure of high-pressure ionisation chambers filled with different types of gases to the radiation field at CERN's CERN-EU high-energy reference field facility. At this facility complex high-energy radiation fields, similar to those produced by cosmic rays at flight altitudes, are produced. The particle fluence and spectra calculated with FLUKA Monte Carlo simulations have been benchmarked in several measurements. The results can be used to optimise the response of ionisation chambers for the measurement of ambient dose equivalent in high-energy mixed radiation fields.