In this work we present a simple pathway to obtain large single-crystal graphene on copper (Cu) foils with high growth rates using a commercially available cold-wall chemical vapour deposition (CVD) reactor. We show that graphene nucleation density is drastically reduced and crystal growth is accelerated when: i) using ex-situ oxidised foils; ii) performing annealing in an inert atmosphere prior to growth; iii) enclosing the foils to lower the precursor impingement flux during growth. Growth rates as high as 14.7 and 17.5 micrometers per minute are obtained on flat and folded foils, respectively. Thus, single-crystal grains with lateral size of about one millimetre can be obtained in just one hour. The samples are characterised by optical microscopy, scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS), Raman spectroscopy as well as selected area electron diffraction (SAED) and low-energy electron diffraction (LEED), which confirm the high quality and homogeneity of the films. The development of a process for the quick production of large grain graphene in a commonly used commercial CVD reactor is a significant step towards an increased accessibility to millimetre-sized graphene crystals.