The official guidance from the College of Arms is clear. So far as "flags on buildings belonging to central and local government" the following should be observed:
On the day of the funeral, the flag should be flown at half-mast from dawn to dusk.
For those interested the general protocol is also covered:
Q. When should the Union Flag be flown at half-mast?
A. Occasions on which the Union Flag is to be flown at half-mast:
- from the announcement of the death of the Sovereign until the funeral
- in the following cases, half-mastings will be by special command from Her Majesty:
- the death of a member or near relative of the Royal Family or the funeral of members of the Royal Family
- the funerals of foreign Ruler
- the funerals of Prime Ministers and ex-Prime Ministers of the United Kingdom
- the funerals of First Ministers and ex-First Ministers of Scotland, Wales and Northern Ireland (unless otherwise commanded by the Sovereign, this only applies to flags in their respective countries)
- any other occasions as commande
- The Department of Culture, Media and Sport will inform Government departments of any other occasions when Her Majesty has given a special command.
Of course overwhelmingly this is being followed. It is something that decent people of all political persuasions wish to respect.