A lot of this may be explained by the booking system reserving seats whilst people go through the purchase, but not actually finalising. As has been said, there’ll be a certain number of seats at each price, and once they’re gone (or temporarily appear to be gone), the price will go up (and might go back down if the cheaper seat purchase isn’t finalised).
An example from when I booked a train the other day: I found a train and clicked through to reserve a seat, but had to dash out before I paid for it. I came back a while later and my session had timed out, and when I went to book the same train, the price had gone up. I suspected my timed-out session had caused the last seat in that price band to get “stuck” as reserved in the system, so I left it and came back the next day. Luckily, the seat hadn’t been booked and it was back down at the previous price.
No reason why this couldn’t happen on e.g. Easyjet.