Deed poll was sufficient for both of those for a name change for me, as well as for the registry office two months ago. I cannot speak for changing gender though, merely name.

Lots of places are very weird about it though because their staff think we have "legal names". I switched banks over the weird bullshit mine was pulling. The number of looks my piece of A4 with a couple of signatures on it has received from staff that then have to go check with someone that it's actually how it works, my gods. No, I know it doesn't look fancy, it doesn't have to, go ask your supervisor if you don't believe me.