Let's break this down.
The PC leases the land to the charity. What does the lease say (if anything) about future capital expenditure?
Does the charity's governing document include a power to give funds to the PC? If not, this cannot be assumed, as it is a fundamental principle of charity that income must be devoted to the charity's purposes as outlined in its governing document. Even if the money will ultimately be used to improve the charity's premises, the payment would not be legal unless the governing document expressly permits it. A ruling from the Charity Commission would be required. Think of the wider money laundering implications of charities being allowed to raise funds, claim Gift Aid, then distribute the money to other individuals or organisations.
Gift Aid allows charities to reclaim tax on donations from individuals towards their work. It is highly unlikely that HMRC would permit a Gift Aid scheme to be used as a fundraising vehicle for a third party, particularly a third party that is ineligible to claim Gift Aid in its own right. A ruling from HMRC would be required.
Any charity operating a public appeal is required to notify potential donors of the purpose for which their donation will be used. If the intention is to hand control of the donation to a third party, this fact should be made available to potential donors as part of the appeal literature.
Looking at the VAT scenario, if the charity gives money to the PC to secure improvements to its premises, is it commissioning work via a third party? If so, the PC is acting as agent to the charity for that part of the project, which brings into question the VAT concession that covers only the PC's own expenditure. The fact that the PC also owns the asset makes that an unanswerable question, so a ruling from HMRC would be required.
Clear as mud!