We're in the early stages of planning a 'backpacking through England' trip. It looks liked we'll be somewhere in Scotland for the 'Early May Bank Holiday' on May 5. The idea is to take the train some place, wander around a bit, and then stop by the tourist office to find a hotel or take the train to the next town. I'm trying to find out if it would be completely impossible to find a place to stay on the nights around that long weekend.
It depends on where you will be, but it won't be completely impossible to find a place to stay any more than it would be on any given three-day weekend here.
Calling or booking online with any listings that you have can help, even a day ahead or on the day of arrival. The flexible attitude of being willing to try another town can be a back-up plan, as long as you arrive by early afternoon, when there are still trains that could get to the next town before the tourist office closes. The British Tourist Office used to publish nice regional maps showing B&Bs, but that search function is now on their web site.
In several European countries (including Ireland but not Scotland) we've sometimes stopped in the tourist office (T.I.) in one town and they booked us a room in the next town down the road, or the town past that one. That gave us time to get to our lodging for the night but not miss the times the T.I. was open, or miss getting a room. A few times they had to check with more than one place before finding us a room, but we never had to sleep under a bridge :-)