Did the pilgrims establish the first permanent English colonies in north America?

No, they did not.
The London Company (also known as the Virginia Company) founded Jamestown in 1607. However, Jamestown was not the first English colony - St. John's and Harbour Grace, Newfoundland, Canada were settled permanently in 1583. The Roanoke Colony in http://wiki.answers.com/Q/Who_founded_the_first_colony_in_north_America_at_1607# was established in 1587 but was unsuccessful as a result of the disappearance of its colonists, which is why the Roanoke Colony is often referred to as the "lost colony".

St. Augustine, Florida is the oldest permanent European settlement in the continental U.S., settled in 1565 by the Spanish.

However, the actual first permanently settled colony in North America was http://wiki.answers.com/Q/Who_founded_the_first_colony_in_north_America_at_1607#, Mexico in 1519. ~ answers.com lol