Edit: Grammatical problems, fleshing out some terms, corrections.

In order to answer this one has to understand exactly how the British government legally divided their holdings.

One of the responsibilities of the King of England was to distribute the land of the country as he saw fit. This was accomplished with royal charters, documents that legally divided the land in question into one of four types of colonies that could be administrated as their prerogative necessitated. These were (In no particular order):

Proprietary - Facilitated financial investment and self-governance, basically a way for the King to pass off the responsibility of a settlement's administration to his political allies/ organizations. These men/ groups could govern as they saw fit and the people living there were subject to English rule but didn't always enjoy all the rights of Englishmen. Examples of these colonies are New York (Founded by The Duke of York) and Pennsylvania (Founded by William Penn), both under Charles II.

Crown (Royal) - Governed by a royally appointed magistrate/ governor who ruled with the authority of the monarch. These colonies were true extensions of royal authority overseas, and their colonists were viewed more as English citizens. A concrete example would be Georgia (Founded by James Oglethorpe).

Joint Stock- High-Risk, High-Reward business ventures formulated as investments from several companies back in England. These eventually became absorbed into the sphere of English rule for the sake of consolidation. The most famous example would be Jamestown.

Covenant- Puritan colonies in which a covenant was signed on its founding that ensured mutual respect, self-sufficiency, and as much independence as possible from the British motherland (And by extent, the Church of England.) The most famous example is Plymouth. These also became absorbed by proprietary/ royal colonies.

Now that we know 'how' and 'why' the colonies could be/ were settled, we can delve into the 'when' and 'where.' Colonies could really be made by anyone so long as they had the funds and will to do so. They were founded in various locations, but oftentimes near running water, the sea, or around some attractive land for agriculture and cash-crops. Dozens upon dozens of colonies were formed in North America alone, the technical 'first' being Roanoke in 1586, the first 'successful' one being Jamestown in 1607, and the last being British Columbia in 1866. (As pointed out by someone in a reply, this was actually a merger of two other previously formed colonies but I considered it as "The last colony that was made in North America" which was true but certainly didn't cover it all. I do apologize for being misleading.)

To answer your question, until 1866, one could in theory sail the sea, land at any number of ports, travel across the expanse of territory claimed by Britain (By this point it was just Canada), and settle a new colony. After that point all of the land that was worth grabbing was grabbed. Throughout the roughly 300-year period of colonization it was never really 'illegal' to settle so long as you had your charter and enforced English law, and while technically you were within your rights to trounce off into the unclaimed wilderness and 'found' a colony whenever you pleased, for obvious reasons it was highly discouraged. (This point was also unclear and I didn't realize at the time. You still needed permission to go settle anywhere, but once you had that permission you could legally settle.)

Sources:

http://www.u-s-history.com/pages/h572.html

http://www.digitalhistory.uh.edu/disp_textbook.cfm?smtID=2&psid=3579

Bridenbaugh, Carl. Early Americans. New York: Oxford University Press, 1981

Nicholas Canny, The Oxford History of the British Empire: Volume I: The Origins of Empire: British Overseas Enterprise to the Close of the Seventeenth Century , 2001,

Followup question: what happened to migrants from England upon arriving to the United States, only to find it no longer a colony? (circa 1778ish) could they be rejected from the country and sent back to England?

This is as much a follow-up question as a response, but it feels like the premise here is somewhat fundamentally flawed? Like would it really be right to characterize the establishment of overseas colonies by force as ever having been strictly "legal?" I would expect the more useful question to be at what point were the colonies already there established enough that they considered new ones to be an intrusion.