No, charities are not normally permitted to engage in non-charitable trading and, subject to certain limits, could be taxed on any trading income.
Larger charities which have significant non-charitable trading income get around this by doing their trading through wholly-owned subsidiary companies which give their profits to the charities before taxation. If a charity is in this category, our suggestion is that their trading subsidiary becomes an additional party to the Agreement, in which case the "Application for Charities which have a Trading Company" should be used.