We used a combination of public RR Lyrae star catalogues and a Bayesian methodology to derive robust structural parameters of the inner halo (<25 kpc) and thick disc of the Milky Way. RR Lyrae stars are an unequivocal tracer of old metal-poor populations, for which accurate distances and extinctions can he individually estimated and so are a reliable independent means of tracing the population of the old high-[alpha/Fe] disc usually associated with the thick disc. In particular, the chosen RR Lyrae sample spans regions at low galactic latitude towards the anticentre direction, allowing to probe the outermost parts of the disc, Our results favour a thick disc with short-scale height and short-scale length, h(z) = 0.65(-0.05)(+0.09)) kpc, h(R) = 2.1(-0.25)(+0.82) kpc, for a model in which the inner halo has a constant flattening of q = 0.90(-0.03)(+0.05) and a power-law index of n = -2.781(-0.05)(+0.05). Similar short scales for the thick disc are also found when considering an inner halo with flattening dependent on radius. We also explored a model which the thick disc has a flare and, although this is only mildly constrained with our data, a flare onset in the inner similar to 11 kpc is highly disfavoured,