One of the big reasons that I get a letter showing my ex's "permission" to take my girls to Scotland is that it builds a paper trail, a record of me asking, a record of him giving consent, a record of me returning when I said I would. It means that if he ever decides to try and convince a judge that I'm going to 'do a runner' with the girls, I can produce a written history of my trips with the kids and the fact that he gave his "permission" each time.
Like I said, you likely won't be asked to produce any such letter. And if it's the word 'permission' that bothers you, try changing the wording to something like "I, Elijah's father, have been notified that he will be travelling to the UK with alzbabybird, Elijah's mother, leaving on such-and-such date and returnging such-and-such date. Blah, blah, blah...."
(I usually word the letter so that it gives the girls permission to travel out of the country with me, rather than giving me permission to travel out of the country with the girls.)
This really covers you as much as anything else....he won't be able to claim that he wasn't fully informed if you've got a piece of paper, notarised and with his signature on it, acknowledging that he has....