The answer on this, unfortunately, will be that it depends. That is, it depends on what the IP clause in the contract specifically states. Do you have a specific contract or clause that applies to this situation?
The clause reads as standard;
"all Intellectual Property conceived or made by X in the course of providing the Services shall belong to Y."
The problem is that the project is being funded by a third party, and part of our agreement with that third party is that they will own all IP arising from the project. We are contracting with another party to deliver one element and our funder is asking that we name them as the owner of IP in the abovementioned clause in the contractual agreement between us and the other party.
Usually the only parties that have any rights to the IP are those parties to the contract. Should another party want access to the IP then the best way to protect the first two parties is that the third also becomes a party to the contract or another way is that the third party enters into a confidentiality agreement with the first two parties explicitly for the purposes of accessing the IP.
In your case you might need the separate agreement as the people you have contracted to may not want to share or assign any rights to their IP with the project financier.