Had a hell of a time trying to get DS's Australian passport renewed last year, they needed consent from ex-arsehole with no PR who hates me and hadn't seen DS for two years! Of course he didn't consent! Had to get a letter from CAFCASS to get one in the end.
Applied for a UK passport for him and they couldn't care less who his father was, no PR meant no say in the matter.
But I was warned that regulations are going to tighten, and we may have a similar system in place to Australia before too long, If your exe's are tw*t's, get the applications in soon just in case.
I bet there are a lot of lovely men out there who would love to stop you taking a holiday with your own kids, while they're laughing about it in the Maldives with their new girlfriend. And banging on about their "rights".