May be you should read my post again; specifically the bit about the fund being a NON PROFIT making organisation and therefore exempt from corporation tax.
According the Companies House web check it is set up as such.
So if it pays corporation tax it is not a non profit making organisation.
Alice - the company in question is a company limited by guarantee. It is generally termed a "not for profit" company because the shares (and therefore the shareholders) do not benefit from an increase in the value of the shares (and thus turn a profit by virtue of their ownership of the shares).
However, this does not mean that the company cannot engage in activities (eg trading in goods, provision of services) which will create a profit, and if it does so then those profits (correctly termed a "surplus) will be subject to tax - Corporation Tax. (unless of course it is a registered charity in which case it will be tax exempt).
If you look at the accounts for the comapny in question you will see that in the year to 2013, they did in fact pay CT of £9756.
There is an exception to this - Small, not-for-profit, non-charitable CLG are allowed to carry on a trade purely between its own members. They are deemed to trade "mutually" and as such are exempt from Corporation Tax. Clearly this does not apply to the Madeleines Fund.
http://www.mccannfiles.com/id474.html