Semi-speculative but hopefully of interest to some...
The information on Companies House is not quite sufficient to put together exactly what has gone on here but the diagram below is my best guess.
The figures in black are based on information from Companies House or press reports in terms of who owns what. It looks like the Staveleys and Reuben Brothers come in at JV1 Limited, owning 10% each with the PIF owning 80% via a UK company called NCUK Investment Limited. There's probably a few more intermediate companies between PIF and NCUK but these will be outside the UK so not publicly visible.
From the Companies House information, there is £622k of share capital invested into JV1 Limited, but JV1 Limited then puts £306.1m into PZ Newco (which is the company that bought Newcastle for a reported £305m). There is therefore a gap of £305.5m (minimum) to fill and I am assuming that money comes by way of shareholder loan(s) - shown in red. I've shown this as coming proportionately from each of the investors - this isn't visible from the Companies House documents and probably won't even be obvious when the first sets of accounts are published. It's likely there'll be a bit more than the amounts shown as well so they can cover the legal fees etc on the transaction.
It's also possible that a bank may have lent some money to PZ Newco, with a corresponding reduction in what the shareholders have put in. This would be the more normal structure for this kind of investment, but I've not seen any reference to bank involvement and I would normally expect another company between JV1 and PZ Newco if the bank is involved (this is referred to as a "Buffer" company and is quite standard for legal / banking reasons in this kind of structure).
There don't appear to be any preferential rights attached to the shares - as far as I can tell, all three investors in JV1 all participate on the same terms (which also suggests they might all be putting some debt in to keep things even).
So this doesn't shed any light on the angle each of the investors have but it looks like, proportionate holdings aside, they're all in on the same terms. My best guess is that the Staveleys, via their investment vehicle, are rewarded with a stake for their role in setting up the deal and this may attract investors in their managed fund. Their investment vehicle isn't a personal one as far as I can tell so there are probably multiple investors behind it (pension funds, high net worth people etc).
Not sure whether there is a property angle for the Reuben Brothers, but if there is then they don't appear to be getting any special return for it - they've been brought in on the deal on the same terms as the others and probably this has been for the expertise they can bring that will benefit everyone.
The big proviso to all of this is that I
assume they are all in on the same terms re the debt investment. The amount of debt invested and/or the terms of that debt could skew the economics towards one or other parties. For example, if all of the debt comes from the PIF, then the Staveleys and Reuben Brothers would only get a share of the profits once the interest is covered. Unfortunately, we won't be able to get any idea on this for a year or so when the first set of accounts are published.