The following is the Fire procedure from CP3 Chapter 4 : Part 1 1971,
AT ALL TIMES
Keep the passages and hall clear of obstructions, particularly of combustible goods and any form of `naked flame' heating. Use the rooms only for the purpose, for which they were intended, e.g. steeping, cooking, etc., not, for storage or as workshops.
IF A FIRE BREAKS OUT IN YOUR DWELLING
l. Leave the affected room at once, together with any other occupants, and close the door,
2. Do not stay behind to put out the fire unless you are sure you can do so safely.
3. Alert occupants of other rooms in the dwelling.
4. Leave the dwelling, closing the front door, and give the alarm (see below). Use the stairs, not the lift. Balconies should not be used unless they form part of an escape route.
IF A FIRE IS EVIDENT OR REPORTED ELSEWHERE
You will normally be safe to stay within your flat. You should close doors and windows, but in the unlikely event of smoke or heat entering the flat before you are able to do so, leave at once closing the doors behind you.
You may have confidence that you will be safe if this is done and it is your responsibility to other occupiers to do so.
This is why I think the terminology should be "stay put if it is safe to do so" and not "stay put".