From the north to the south, Britain stretches for approximately 700 miles. Assuming I have a single horse, and enough money to buy whatever I need along the way, what's my rate of travel? How many days would it take for a rider to reach from one end of Britain to the other? Assume whatever period you'd like, as well as any supplies necessary. I'm just curious as to the rate of travel in, let's say, the sixteenth century.
Sixteenth century: roads are improved dirt at best. In many places, they aren't that good. But at least a sunken lane is something you can follow. Many a moor is literaly pathless, trackless. Some towns had stone land lighthouses in which a fire could be lit to guide expected travellers. Many villages were barely known to exist outside their bounds, & they liked it that way. Remember how war had washed back & forth. Strangers meant tax collectors or armies. So you are going to stick to the major streets all you can, which can add some considerable mileage.
In summer roads are very dusty, in spring and often autumn deep mud. In winter, in the pits of the Little Ice Age, snow may be up to your horse's belly. So let's say summer, the fastest time to travel.
You are travelling on an animal that needs food, water, rest, and sleep. You are going to walk, trot, and occassionally canter, take hourly and noon stops, making about thirty miles a day. I'm basing this much on The Traveller's Oracle, and a lot of Old West reference, not to mention Smiles' chapters on the previous state of British roads in his bio of Thomas Telford.
700/30 = 23 1/3 days and you can get a fortune for that horse.
Now someone may bring up the old USA cavalry boast of "Forty miles a day on beans and hay." But that's 19th C horses. In the 1500s, you don't even have Thoroughbreds begun yet. 20 miles a day is more likely.
700/20 = 35 days, and that all assumes your horse doesn't go lame from various causes and you don't get held up by petty officials who don't like the looks of your travel papers.
European horses may never have been up to USA cavalry remounts. In the later 1800s, a friendly little race was run by German and Austrian riders, as to who could ride fastest between Berlin and Vienna. They rode with minimal equipment their choice of horse, from Thoroughbreds to Hungarian steppe ponies. The winner did it in three days, the others trailing in after three days and three hours and beyond. Every horse in it died or was permanently ruined by the strain. An author wrote about this in 1898, with a huge collection of better performances while packing full Army tack and gear, including weapons & ammo.
So much depends on the horses, the roads or their lack, the weather, and how hilly the route is.