Travel was not an easy thing before the late-19th century. It wasn't just the lack of fast vehicles, but that roads were terrible back then; most were heavily rutted and often impassable, and travelers were very limited by the weather because it only made it worse. Toll roads were introduced in the 1600s to help pay for the cost of upkeeping the roads, but the technology wasn’t good enough to keep the roads in good condition. And in the end, tolls slowed down traffic (because of the need to stop and pay) and increased the cost of travel significantly.
Before 1805, a 50-mile journey by coach took 14 hours. By 1830, it took about 8 hours, though the Royal Mail Coach could do it in 5. Before 1840, it was common for a 175-mile journey to take 10 days by private coach, though the Royal Mail could make the journey in 16.5 hours. Generally, the Royal Mail could cover 100 miles in 11 hours and 200 miles in 26 hours.
When traveling long distances, there were a few options available. Private carriage travel was slow but generally more comfortable. The owner has the luxury of setting their own timetable and travels from door-to-door. Plus the carriage can be used at the destination, once they'd arrived. However, it was the most expensive option. Between food, accommodations, horse hire, staff expenses, tolls, etc., it was very pricey and was generally reserved only for the wealthy.
The Royal Mail Coach was introduced in 1784 to transport mail across the country and was the fastest and most reliable form of long-distance travel until the advent of the railroad.
These coaches did not have to stop for tolls and all other vehicles were required to give way for them, meaning they were the quickest on the road. If you've driven in the British countryside, you can still see how that works as many roads in the countryside still function this way. The roads are one lane wide with turn-offs at regular intervals; when you come across on-coming traffic, one of the vehicles pulls into the turn-off to let the other pass. As the Royal Mail Coach never had to give way, they could travel a lot faster. You might be thinking to yourself that it wouldn't make that much of a difference in travel time, but as someone who has spent hours driving through country lanes in the UK, I can tell you that it makes a huge difference.
While it was the fastest way to travel, tickets were expensive enough that only the gentry could afford to use it. Plus, the Royal Mail Coach's primary purpose was transporting mail, so they only took on four passengers, which made tickets harder to get. On top of that, they didn't have extensive routes, so travel could only be done between main cities, which wasn't always convenient for travelers.
The Stage Coach was the most common form of long-distance travel. It was fairly reliable and offered more routes than the Royal Mail. However, it had to stop at all tolls and was more dangerous than other forms of coach travel because there were up to twelve passengers sitting atop the coach (instead of mail bags), making it very top-heavy; accidents were fairly common. This was the option that was most common for the middle class and upper-level servants (such as butlers, housekeepers, governesses, etc.).
If you couldn't afford one of those three forms of travel, you were out of luck until the introduction of the railroad in the latter half of the century. Most people in the lower classes didn't travel, and if they did, they walked or begged a ride off passing wagons. It was common for freight wagons to take on passengers if they had space, but travel was at a walking pace and uncomfortable (and smelly, depending on the cargo).