Media lawyer Paul Gilbert has told Daybreak that judges will have to decide on "whether or not a tweet itself is more than shocking or offensive."
He added: "It's finding a balance between what the law says about this and the freedom of speech."
More top news
The true number of those believed to be dead or missing and presumed dead following the fire won't be known until the end of the year.
Low pressure will keep much of the British Isles under cloud with many seeing periods of steady rain throughout the rest of today.
Michael Bond, the creator of Paddington Bear has died at the age of 91.