I saw this old B&W movie the other day; Richard Widmark and Sydney Poitier starring. What surprised me was that all real warship shots were that of a British Type 15 Frigate. the pennant number was clearly shown but I didn't have presence of mind to remember it. All real warship exterior shots also seemed to be filmed on this ship or another UK warship as items such as WT doors were definitely British. All model shots of the 'starring ' warship were that of a US destroyer.
I found it odd that they used a UK ship for the exterior shots, except of course the US military does not lend its assets to films where the US military is shown in a bad light; they refused to help with Crimson Tide for the same reason.