Yes, at the table. This is the person who is authorized to issue the certificate.
I would like to answer your question about the person who shows up at the inaccessible polling station at 7:50 p.m. In such a situation, the returning officers and clerks take out the ballot box and allow the person to vote then and there, so that he or she does not lose his or her right to vote. If the person is already registered at the polling station, there isn't a problem.