Permission from one parent when other taking DC abroad?

[NotaDisneyMum]

I've just seen something in LP that's made me twitch and my Google search has left me even more confused!

In cases where there is no CO for residency, does a parent with PR need the written permission of the other parent to take the DC out of the country?

My DD (UK passport) is going abroad with her dad, his partner and other family members next week; I've said it's ok verbally but not signed anything - could they get stopped and be refused travel?

i went to india to see my family and took dd with me. dh and i are married but while applying for a visa i needed to get dh's permission on a letter with his signature.
bizzare but i guess some parents just take the kids away without the others knowledge.