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The Pristine survey uses narrow-band photometry to derive precise metallicities down to the extremely metal-poor regime (⁠|$ \rm [Fe/H] \lt -3$|⁠), and currently consists of over 4 million FGK-type stars over a sky area of |$\sim 2500\, \mathrm{deg}^2$|⁠. We focus our analysis on a subsample of ∼80 000 main-sequence turn-off stars with heliocentric distances between 6 and 20 kpc, which we take to be a representative sample of the inner halo. The resulting metallicity distribution function (MDF) has a peak at |$ \rm [Fe/H] =-1.6$|⁠ , and a slope of Δ(LogN)/ |$\Delta \rm [Fe/H] = 1.0 \pm 0.1$| in the metallicity range of |$-3.4\; \lt\; \rm [Fe/H]\; \lt -2.5$|⁠. This agrees well with a simple closed-box chemical enrichment model in this range, but is shallower than previous spectroscopic MDFs presented in the literature, suggesting that there may be a larger proportion of metal-poor stars in the inner halo than previously reported. We identify the Monoceros/TriAnd/ACS/EBS/A13 structure in metallicity space in a low-latitude field in the anticentre direction, and also discuss the possibility that the inner halo is dominated by a single, large merger event, but cannot strongly support or refute this idea with the current data. Finally, based on the MDF of field stars, we estimate the number of expected metal-poor globular clusters in the Milky Way halo to be 5.4 for |$ \rm [Fe/H]\; \lt\; -2.5$| and 1.5 for |$ \rm [Fe/H]\; \lt\; -3$|⁠ , suggesting that the lack of low-metallicity globular clusters in the Milky Way is not due simply to statistical undersampling. [ABSTRACT FROM AUTHOR]