Nope. The Cross Keys has records from 17th century of an Inn being on the site, but not in the premesis. A slight technicality. The No Sign is the oldest pub.
Established in 1690. The No Sign featured in Dylan Thomas’s short story “The Followers”. The Reason why it's called No Sign. Public houses selling alcohol had to have a recogniseable sign. However as the building was a bar and not a public house, a sign had not been allocated. This was soon rectified and the premises was officially presented with the title of “No Sign” by officials