That's too bad the Turf Tavern doesn't work—it's such a cool place and very historic. And the food was very good, as was the beer. I really liked it. Eagle and Child has been closed for a year or more. I'm not sure it will reopen.
I will say that most pubs are going to have similar menus to the Turf Tavern, so you may want to look for a regular restaurant or cafe. Is there a particular food that your friend can't eat?
Regardless, there is also the Bear Inn, which is another very historic pub not too far from Christ Church. Oops, never mind - it's closed for renovations until early July.
There's St Aldates Tavern nearby. I haven't eaten there, but the reviews are decent.
That said, I just noticed that you will have 10 people. That's going to be difficult to find something last minute on a Saturday lunch in June in Oxford. I would strongly suggest calling around or stopping by early to see if any place can accommodate a large group like that. You may not be able to be too choosy.