Quite right. And wildly enough, the oceans are also swimming with food. :^) The good old ancestors who crossed during the Great Migration spent a month or more making the passage (the surname ancestors embarked in February and arrived in March, so the food wouldn't have spoiled anyway), and those boats were stuffed, given their size. No one would but a refugee would travel that way today.
Of course, the diet of the average lower class Englishmen in the 18th and early 19th Centuies was pretty wretched. A number of sailors joined the Navy because the food was better than that at home.