Booking v Winging it

unpublished reasonable rates

Do you mean on train or bus? If so, nope.

Do you mean in hotels? If so, the rates are dependent on how busy they are. If the rooms are full the rates stay high. If they aren't so nice and people don't stay there they have to lower the rates to entice people in.

Or if the weather is good people stay away from home more. If the weather is bad people stay home.

At the end of the day people who don't book ahead get what is left over from those who do.

Advantages both ways....

There was a time, in the '80s and maybe early 90's, when you could just wing it. We did it often, in the UK, in France especially, and other west European countries. If we travelled by car we just headed for the railway station in any town and found lists of hotels and B&Bs, or drove around town looking for "Hotel" signs. But with the number of tourists these days, and NOT just from N. America, (important to consider) I fear you will waste a lot of time "winging" it and end up in some unsavoury hotel rooms. But, hey, maybe you don't mind unsavoury ......

I live in the UK and I would not risk UK travel in May/June without prebooking, much less do so abroad.

Why spend half your holiday trying to book rooms? The best rooms will already have gone by now, as Europeans tend to book holidays much earlier than Americans seem to, particularly for the Bank Holiday. You will probably get some availability at the faceless chains such as Hilton, but weekends will be trickier. Prices at chains such as Premier Inn and Travelodge increase the closer to the travel date.

All room rates are published, so I am not sure why you think that places wouldn't do so. The only chance you have of a late discount is if the weather is poor so people decide not to travel or if a place is less popular and availability remains. Popular places such as Bath, York, Edinburgh etc have less reason to discount. You may get discounts in non-touristy towns last minute, but these are towns that are probably not on your itinerary.

I'm a big proponent of advance booking (thank you, internet)...that being said...if you are travelling with a smartphone/tablet and have access to wifi...it makes it a little easier to wing it. You can always go on a site like hotwire (usually good last minute deals from places trying to book up that last room) or expedia or booking.com and see what you can get the next day or two if you decide you want to stop in a certain spot. Keep in mind, you may not find something within your budget in the area you want to stay - or you may end up somewhere dodgy because everything 'good' is booked.

Our trip to California we had two nights that we didn't book because I wasn't sure where we would be in our travels. The night before, we'd look at a map and say...let's stop here and I'd get out the iPad and book something via expedia...I could always find something in my budget - but it was usually a chain hotel/motel, nothing cute and quaint.

There is a website called Late Rooms which is particularly good for locating available rooms on the day, although you can also use it for booking in advance. They have an app for phones and tablets which will identify where you are located and then show what rooms are available in the vicinity at that moment, together with their prices.

The available rooms are shown on a map, so you can decide which place best suits your requirements. You can also type in your destination to see what is available to suit your needs.

In London pre-book!! If you are driving around the country side you can wing it. I've been in the UK many times in June and July, have never pre booked while driving. You can go to the tourist information center in villages and they can book a B&B for you, or just drive and watch for B&B signs when you decide you want to stop for the night. We have never ever had a problem finding a room.

We had the same experience as Robin. We always booked London. We prefer B & B when we drive. Sometimes the host of a B & B will call ahead for you to book with one of their fellow hosts. When you drive you can stay out in the country and then drive to town.
Some of the out of the way places offer full board: Breakfast and Dinner and sometimes a box lunch or an afternoon tea. You can get listings by region. Not everyone (but probably most) is on-line. But be advised the popular Tourist areas may be overrun by the "new travelers", but they are more likely in groups so will be at hotels. So go to out of the way places to have a more unique experience. If you are taking the train only, you will probably have to book ahead just for peace of mind. Buses are usually best used for local travel.

Since the poster clearly stated that they will be traveling by bus or train, I don't see what relevance is of responses about just driving to any place can be. Besides bank holidays, there can be local festivals which fill up everything. Here's an example: One weekend when we were living in London, we decided to go to Brighton sans reservations. Surprise! It was the Brighton Festival weekend. TI office had no places for us; however, we had a car. They called the next town and found us a perfectly fine hotel, at a perfectly fine price, which we were able to drive to. Worst case, we could have driven back to London at the end of the day. All would have been much harder if not impossible without the car. Personally, I wouldn't chance it.