  (abridged) In this paper, we constrain the properties of primordial binary
populations in Galactic globular clusters using the MOCCA Monte Carlo code for
cluster evolution. Our results are compared to the observations of Milone et
al. (2012) using the photometric binary populations as proxies for the true
underlying distributions, in order to test the hypothesis that the data are
consistent with an universal initial binary fraction near unity and the binary
orbital parameter distributions of Kroupa (1995). With the exception of a few
possible outliers, we find that the data are to first-order consistent with the
universality hypothesis. Specifically, the present-day binary fractions inside
the half-mass radius r$_{\rm h}$ can be reproduced assuming either high initial
binary fractions near unity with a dominant soft binary component as in the
Kroupa distribution combined with high initial densities (10$^4$-10$^6$
M$_{\odot}$ pc$^{-3}$), or low initial binary fractions ($\sim$ 5-10%) with a
dominant hard binary component combined with moderate initial densities near
their present-day values (10$^2$-10$^3$ M$_{\odot}$ pc$^{-3}$). This apparent
degeneracy can be broken using the binary fractions outside r$_{\rm h}$- only
high initial binary fractions with a significant soft component combined with
high initial densities can contribute to reproducing the observed
anti-correlation between the binary fractions outside r$_{\rm h}$ and the total
cluster mass. We further illustrate using the simulated present-day binary
orbital parameter distributions and the technique introduced in Leigh et al.
(2012) that the relative fractions of hard and soft binaries can be used to
further constrain the initial cluster density and mass-density relation. Our
results favour an initial mass-density relation of the form r$_{\rm h} \propto$
M$_{\rm clus}^{\alpha}$ with $\alpha <$ 1/3.
