I think the movie is the 1977 USA/Japanese co-production The Last Dinosaur. Rankin and Bass (of Rudolph, The Red Nosed Reindeer fame) financed it. Your description of the ship matches well the Polar-Borer that takes the explorers through the Earth's crust to a prehistoric land in the Artic. Did the ship look like the one in the pictures below? The dinosaur does attack their ship at the beach and carries it away in its mouth, stranding them on the island.

The Last Dinosaur is a color movie. The effects are very much in the Toho style. The T-Rex is a very unconvincing man-in-a-suit. That is why you may associate the dinosaur with Godzilla. The movie never played in movie theaters in the states. I remember watching it repeatedly on network and local television in the late '70's and early '80's. It has a largely American cast, so the lead actors speak their own lines without dubbing.

Richard Boone stars as an oil tycoon (and big game hunter) who finances a scientific expedition to explore a recently discovered prehistoric land at the North Pole. A very active volcano has kept the area a tropical paradise for millennia and it is inhabited by prehistoric creatures and cave people. Both attack the expedition. Boone becomes increasingly more savage and threatens the other team members. All he wants to do is hunt and kill the last T-Rex on Earth, while the others want to recover their ship and escape. Joan Van Arc (from television's Knots Landing) plays the lead scientist.

The original, un-edited cut of the movie has been released on DVD. I found two good reviews of those DVDs here and here.