Interesting that the Public Order Act 1986 (which prohibits actions intended to cause harrassment, alarm or distress through the use of threatening, abusive or insulting words or signs) has been used to charge the individuals responsible for the vile video mocking the Grenfall residents. I've only ever come across this being used for verbal or written (including electronic) words, that's not to say it's never been used for offensive videos before.
https://www.bbc.co.uk/news/uk-46106224
I had assumed that they would have used the Communications Act, which carries a prison sentence of up to six months.