We construct the Type Ia supernovae (SNe Ia) luminosity function (LF) using the Zwicky Transient Facility Bright Transient Survey (BTS) catalogue. While this magnitude-limited survey has an unprecedented number of objects, it suffers from large distance uncertainties and lacks an estimation of host extinction. We bypass these issues by calculating the intrinsic luminosities from the shape parameters of the light curve's g and r bands, with the luminosities calibrated from the well observed SNe Ia sample of the Carnegie Supernova Project, allowing us to construct, for the first time, the intrinsic LF of SNe Ia. We then use a novel tight relation between the colour stretch and the synthesized 56Ni mass, MNi56, to determine the MNi56 distribution of SNe Ia. We find that the LFs are unimodal, with their peaks in line with previous results, but have a much lower rate of dim events and luminous events. We show that the features on top of the unimodal LF-derived distributions are all compatible with statistical noise, consistent with a single progenitor channel for the explosions. We further derive, for the first time, the SNe Ia distribution of host galaxy extinction, and find a mean selective extinction of E(B-V) ~= 0.1 and a non-negligible fraction with large, >1mag, extinction in the optical bands. The high extinction is typical for luminous SNe, supporting their young population origin.