The responce I recived was.
"The picture was taken from a public place/right of way and hence within the law. Quite apart from Geograph, much more detailed photographs of the overwhelming majority of houses (including your barn) in this country are published on the Internet in Google Streetview; whilst photographs of the whole country in plan view (including your property) may be seen on Google Earth. Consequently, I am unwilling to accede to your request."
I responded with:
"You are of course correct that google earth and street view both contain images of my property they do so equally for everyone and if I so wish I can request that they remove this information. The issue here however is that when I google image search my property by name the only related picture to be returned is yours. This I find an unreasonable and disproportionate intrusion into my privacy."
to which I recived:
"The Geograph project aims to collect geographically representative photographs for every square kilometre of Great Britain and Ireland and our aim is to preserve this information for future generations. In order to ensure the project's long-term survival, our website is archived for preservation by the UK Web Archive project. We have to date collected 4,575,280 million images, including thousands of pictures of private properties viewable from public places - a site search for "house" found 585,310 and a search for "dwelling" resulted in 216,585 images; there are 47,817 pictures of barns."
They have amended the text surrounding the image to exclude my house name but this hasnt removed it from the google seach result as they correctly point out this may take weeks or months. Removing the image from there site however would considerably assist in this but they are not willing to proceed on this basis.
Hope this helps and thanks for your time.