In your request for permission that you sent to the Conservative party you wrote: "I am writing to ask the permission of the Conservative Party for the use of this image (solely for this not-for-profit project) since I assume it is copyrighted.". I am afraid that is not enough. The photos on WikiCommons must be made available for use outside the Wikimedia projects, eg. including any commercial use. The reply you received is also clear enough: "I am happy to give copyright consent for your usage as outlined.". I have today deleted the photo.