New neutrino-nucleus interaction cross-section measurements are required to improve nuclear models sufficiently for future long-baseline neutrino experiments to meet their sensitivity goals. A time projection chamber (TPC) filled with a high-pressure gas is a promising detector to characterise the neutrino sources planned for such experiments. A gas-filled TPC is ideal for measuring low-energy particles as they travel much further in gas than solid or liquid neutrino detectors. Using a high-pressure gas increases the target density, resulting in more neutrino interactions. This paper will examine the suitability of multiwire proportional chambers (MWPCs) taken from the ALICE TPC to be used as the readout chambers of a high-pressure gas TPC. These chambers were previously operated at atmospheric pressure. We tested one such MWPC at up to almost 5 bar absolute (barA) with the UK high-pressure test stand at Royal Holloway, University of London. This paper reports the successful operation of an ALICE TPC outer readout chamber (OROC) at pressures up to 4.8 bar absolute with Ar-CH$_{4}$ mixtures with a CH$_{4}$ content between 2.8% and 5.0%, and so far up to 4 bar absolute with Ar-CO$_{2}$ (90-10). We measured the charge gain of this OROC using signals induced by an $^{55}$Fe source. The largest gain achieved at 4.8 bar was $64\pm2)\cdot10^{3}$ at stable conditions with an anode wire voltage of 2990 V in Ar-CH$_{4}$ (95.9-4.1). In Ar-CO$_{2}$ a gain of $(4.2\pm0.1)\cdot10^{3}$ was observed at an anode voltage of 2975 V at 4 barA gas pressure. Based on all our gain measurements, we extrapolate that, at the 10 barA pressure necessary to fit 1 tonne of gas into the ALICE TPC volume, a gain of 5000 in Ar-CO$_{2}$ (90-10) (10000 in Ar-CH$_{4}$ with $\sim\!$ 4% CH$_{4}$ content) may be achieved with an OROC anode voltage of 4.2 V ($\sim\!$ 3.1 kV).