Edit: I asked about Britain but I'd love to know about any other place in medieval Europe if anyone knows anything
Let's assume I'm a man and that I am not dirt poor but nowhere near rich; I'm picturing the average townsperson. Maybe I have a wife and kids if that makes a difference.
I'd like to know what this kind of person would require for this kind of "short trip".
I'm guessing this trip would require multiple days and a fair amount of preparation. What kind of gear would be common to bring along for this kind of voyage?Would it be safe to do this alone or would he prefer to go with a group?I'm also guessing that having a horse was costly but doing the trip on horseback sounds massively beneficial. Would it be common for him to own a horse? If not, was there any way to rent one for such a trip?
A really useful resource for approaching your question is the Open Domesday Project, part of which is a digitised map of every settlement named in the 1086 Domesday Book (although admittedly omitting cities and major urban centres). As you can see, travelling 50km wouldn't just take you to the next settlement, but far, far past it and probably past several others as well. Where you get a greater distance is between the Burh sites which, by the late 10th Century, had evolved (or were being evolved) beyond their initial military function into civil centres and mandated sites of high-value trade (see Æthelstan II). Nonetheless, these are still no more than 40 miles away from each other, so that no settlement was more than a day's march from relief by a garrison force. Unless you were travelling from burh to burh, therefore, you're really unlikely to be travelling more than a day. In fact, if you're making a short trip, say, to market in the nearest large town, you might have an early start and a late return but you'd probably make the whole trip in the same day.
A useful illustration can be seen in The Book of Margery Kempe, where Kempe illustrates an anecdote in which she and her husband walk home from a market:
It happened one Friday, Midsummer Eve, as this creature was coming from York carrying a bottle of beer in her hand, and her husband a cake tucked inside his clothes against his chest...
As the rest of the anecdote suggests, this is far more of a casual walk than a long-distance hike.