X-ray phase contrast imaging provides a method to distinguish materials with similar density and effective atomic number, which otherwise would be difficult using conventional X-ray absorption contrast. In recent years, multiple methods have been developed to acquire X-ray phase contrast images using incoherent laboratory sources. The single mask edge illumination setup has been demonstrated as a possible candidate for large scale applications due to its relaxed restrictions on longitudinal coherence and mask alignment, and for its ability to do bi-directional phase contrast images in a single sample exposure. Unfortunately, the single mask edge illumination setup's refraction sensitivity, and thereby signal to noise, is limited by detector artifacts. Furthermore, it requires multiple exposures to perform dark-field imaging, a method that enables imaging of micro-structures smaller than the image resolution. We propose using an Advapix detector with Timepix3 pixel-readout chip in a single mask imaging setup to improve signal to noise ratio in phase contrast images. This is achieved using the Timepix3 chip's ability to simultaneously acquire fast time of arrival and time over threshold measurement of single photon events, which enables sub-pixel identification of individual photons. In this paper, we demonstrate that signal to noise ratio can be improved by at least 67± 5 % using subpixel identification of single photons compared to conventional acquisitions methods. Thereby the required sample dose can be reduced considerably. This shows that there is a great potential in using Timepix3 chip to improve x-ray phase contrast imaging. Further, the results indicate the possibility for dark field imaging in a single sample exposure using Timepix3 in a single mask edge illumination setup.