Nowhere close to it. The early migrants were from Britain but they were vastly outnumbered by later migrants in the 19th century who came in their millions.

Just generally, the reason why people left Britain in the 17th century was of excess labour/crushing poverty. The English Civil War increased mortality so that by the end of the 17th century, few were willing to leave (which led to a change in labour supply for the US of some significance). Migration increased, again, in the early 19th century due to some fairly harsh recessions in textiles employment...but people fled Italy, Ireland, and Germany in far larger numbers because the economic issues there were more severe: crushing poverty, massive overpopulation, no economic opportunity or way to sustain life.

Just quantitatively though, I suppose Mexico is probably close to the biggest actual migrant flow...although that largely reflects the fact that the population is bigger than it was in 1850.