Farthest I have been is 140 miles (yesterday). It was run off in a group, and at a fairly steady pace (17mph av). Felt fine afterwards, and could have carried on plenty longer.
It's quite doable, though I woul;d go out of my mind with boredom if doing it by myself.
If you want to get into this, then doing audaxes is your route. A genuine audax starts at 200km, then they tend to come in at 300, 400, 600 and updwards.
It's all about progression. you won't do it straight away, but a steady progression towards your goal is a good idea. And eating. Stopping for a decent lunch is good, as is regular eating of nice food.
Failing that, enter a 12 hour timetrial and see if you can hit 250 in the time....