I learned the hard way that you have to turn up on time. Whereas there used to be some flexibility that has now gone, and as you experienced it's strictly enforced.
You were lucky to get away with a change fee of 60 pounds. You could have had a fare class where no changes were permitted whatsoever, in which case you would have had to fork out for another ticket.
Take a look at the ticket counter on a normal day in July. It will be full of (annoyed) leisure travellers who have missed their flight and want to change to another flight - now imagine their faces when the family of 5 find out that no changes are permitted on the day of travel and they have to buy a new ticket for all of them.