The City of London certainly has its own coat of arms. Phrasing that as "its own crest" is a bit weird. (The crest is only part, and by no means the most important part, of a heraldic achievement. The escutcheon is the important bit.)

Arms: Argent a cross gules, in the first quarter a sword in pale point upwards of the last.

Crest: On a wreath argent and gules a dragon's sinister wing argent charged on the underside with a cross throughout gules.

Supporters: On either side a dragon argent charged on the undersides of the wings with a cross throughout gules.