This appears to have been at the location of modern-day Cockpit Yard, north of modern-day Theobald’s Road, west of Gray’s Inn Road, north of Holborn Library. More from here about Cockpit Yard:

In a widening at the far end of this Yard was the cockpit commonly known as the Gray’s Inn Cockpit. It had a pointed conical roof and in structure was not unlike a theatre with seating around a central arena. The Gray’s Inn venue was one of the most frequented in the whole of London, attracting nobility from far and wide and many a handsome bet, even by today’s standards, were placed on the duelling birds.