What was the British presence like in the New World before Roanoke? Did the British have scouts sent over to the “colonies” before the settlers that would found Roanoke?

Limited would be a good descriptor. Yes, they did. Those scouts found Roanoke and a few years later they attempted to establish the first permanent English colony upon that spot, with permission from a local tribe.

As a point of clarity, it was the English and not the British that did this and did so under Queen Elizabeth I, who reigned from the mid 1500s to 1603. In 1603 King James VI of Scotland also became James I of England, Wales, and Ireland, making him the first king of Great Britian, which is what the term British refers to. James I is also the guy Jamestown would be named for a few years after his accession and Virginia was named in honor of Elizabeth I, the Virgin Queen, in 1584.

Did anyone seeking their fortune set out on their own before 1587?

Absolutely. John Cabot, an Italian navigator, was sent by King Henry VII to explore the North American east coast in 1497, and he was the first European since the Vikings to do so. After that a series of English individuals or organizations followed across the Atlantic, most of which were searching for the Northwest Passage in order to make a fortune in trading. Then came a man named Humphrey Gilbert, and with the help of some others he began influencing folks into the idea that a colony could hold possession of the passage when it was found. Cartographers like John Dee began publishing maps, some specifically for particular explorers/proto-colonizers, including Gilbert, based on the numerous expeditions that had started with Cabot. Martin Frobisher's 1576 voyage, for instance, was inspired partly by the discourse started by Gilbert in 1566, and Gilbert himself invested in that Frobisher endeavor. Others, such as Francis Drake, had been sailing the Atlantic as well, although he was more of a pirate than an explorer or colonizer. He would be instrumental in the fate of the Roanoke colony, though he was unaware of the role he would ultimately play. A snippet of an earlier post giving a quick overview of this;

In 1566 [Gilbert] had started work on A Discourse of a Discovery for a new Passage to Cataia in which he championed for a trip to find the Northwest Passage to China, cutting in on the Portuguese and Spanish virtual monopoly on the existing routes. The Queen said no, but in 1578 granted Letters of Patent to claim and colonize any lands not actively possessed by Christians in the new world. He set out on a failed attempt to colonize in 1578 which inspired two brothers, one being his half brother Sir Walter Raleigh, to become engaged in the concept as well. After the first failed voyage another was planned, this time in 1583.

The second voyage was also troubled from the start. One of the larger ships almost immediately returned to England due to crew sickness. The rest made it to Newfoundland which he then claimed for the Queen, but soon after his large flagship would wreck and most of his records would be lost. He remained on a smaller ship he had used for coastal and river exploration of Newfoundland for the return voyage instead of moving to a more sea worthy vessel. On the return trip The Squirrel, that smaller ship, would be swallowed by the ocean taking Gilbert and her crew down with her.

At this point his colony rights were split between his half-brother Raleigh and proper brother Adrian, with Adrian getting the rights to pursue the Northwest Passage north of Newfoundland and Raleigh getting the southern portion leading towards current Florida, North of occupied Spanish claims. Raleigh would waste no time, setting out almost immediately in the voyage that would bring Manteo and Wanchese to the London Court and soon after starting the 1st, and later the more popular failed, colonies at Roanoke. He also invented the word "Virginia" in honor of the Virgin queen, which is the land Roanoke was originally on only later becoming North Carolina.

Raleigh was even a participant on that second Gilbert voyage, but his ship - the largest of the fleet - had turned back early in the expedition. A lot of folks had gone by the time Raleigh sent Governor White to establish Roanoke, and the Native Americans Manteo (a Croatoan) and Wanchese (of the tribe that controlled Roanoke Island) had already toured London by that time. Wanchese had returned in 1585 while Manteo stayed in Europe until White's attempt to settle what is know as the Lost Colony of Roanoke, Manteo having been appointed Lord of Roanoke by Raleigh. If you'd like to know more on this, my earlier post about Roanoke may be of interest as well as the link to part two of that write up found at the end of my posts.

I know the Spanish were in Florida before then but what about the British or French? Do we know for a fact that the Native American tribes were the only people to set foot anywhere around the area of the colonies before the Roanoke settlers?

The French tried a couple of settlements as well as uncolonized trading and, as far others in the area of the original british colonies, we actually know the opposite is true as the Spanish had colonies near modern Charleston South Carolina and Jamestown. Early writings also tell us of common trading deals with coastal tribes by Europeans, my favorite story being one where the Natives would "moon" the traders as the traders sailed away. Here is a post snippet about some of that;

Ajacan is another interesting tale. A "colony" established at Bahia de Santa Maria, it had odd origins. The Spanish sought to protect their golden colonies with buffer colonies and to claim their land, La Florida, which extended essentially up the whole North American continent. French huguenots had been trying to settle and had done so in the 1560s at La Caroline (or Fort Caroline), near modern day Jacksonville, FL. Before that settlement a Spanish ship traveled off course to Bahia de Santa Maria - what natives then and modern maps today name Chesapeake Bay - and kidnapped two local young men, one being Paquiquino. They were taken to Spain and exhibited to the Royal Court, being the first Virginians to visit Europe. Technically they actually "explored" Spain before any European explored Virginia. Paquiquino was taught Spanish and educated in Spanish ways, then sent to Mexico city on a brief trip. Four years later and having converted to catholicism resulting from a near death illness, Pedro Menéndez de Avilés, who had established St Augustine after destroying the French at Ft Caroline, took him to establish more colonies. The first was on modern Parris Island (St Elena), and they soon sailed again towards Paquiquino's home. But they missed it and soon were headed east, back to Spain. A third attempt was made, this time under the control of Jesuits seeking to save souls (the powers accused the settlers of conspiring with Paquiquino to avoid finding the place). Menéndez implored them to bring a military garrison along but the priests refused, opting instead to use the bilingual abilities of Paquiquino (who took the name Don Luis de Velasco after his conversion) and their faith in the Lord to guide their safety. They eventually made their way to the Chesapeake, then up Powhatan's River (later named the James) and landed about five miles from the future site of Jamestown. They then hiked across the peninsula to the (again, later named) York River and settled within a local tribe, an Algonquin tribe that had familial ties to Paquiquino. They built a garrison and a chapel, and made a European style palisade. This was greatly preserved by the fact the site was later claimed by the military and is York River Naval Station today, preserving the site from commercial building and the bulldozers that come with it, and allowing William and Mary archeologists to excavate it in 2010.

The timing was bad and the natives didn't have much to spare. Yet the colonists brought little other than the word of God and had no military force to demand tribute with, but expected - just as the English later would - that the locals would be subservient to them and feed them. Paquiquino grew frustrated and stopped helping the Spanish, then left the village. The language barrier went back up as nobody ever bothered to learn his "heathen" language, and the score of settlers were in a very bad spot. After some time, a few went to the village in which Paquiquino was then living but that turned sour fast - those colonists were killed by members of the tribe. Soon that tribe would attack those remaining at the "colony" (which was really just a native village with a "Spanish town" district, in modern terms). One person, a boy, was spared and left to live within the native community. When a Spanish ship arrived and found the destruction of their site and the lone survivor, they took him and executed 40 natives in retaliation. Ajacan had failed. A few years later, Raleigh would land at Roanoke Island and name it Virginia.

For English/British colonial efforts, Alan Taylor's American Colonies does a great job - his title is indicative of his approach that America had numerous colonies, being better described as the American Colonies than the more often used Colonial America, as if it were singular in origin, cause, and culture.

We Could Perceive No Sign of Them by David MacDonald and Raine Waters does a great job of exploring little known failed colonies of North America starting in 1526. The title is actually a quote from Gov White's journal entry about his arrival in Roanoke years after he was forced to return to England in 1587 (only weeks after landing on Roanoke).

Happy to elaborate on anything specific or answer and followup questions.