Is the assumption that a fire downstairs would not start in the hall
and that all room doors would be shut, thus containing the fire for a
short while?

Yes. Which is why closers are required. Should the fire start in the hall
(which is exceedingly rare) or the self closers have been defeated (very
common), the secondary escape method comes into force. This is having a 30
minute fire protected loft with escape window that you may be rescued by
firefighters through.

Do the stairs from the ground floor then have to be boxed in?

Normally. The staircase doesn't need protecting from hallways. But it does
need protecting from rooms, unless it is using the 2 escape routes to
outside door method.

I don't follow the intent here.....

The idea is that you usually have a protected route (or 2 independent
unprotected ones) to an outside door so that you may escape. If using
protection instead of doubling up, it shouldn't be open plan into a room
which could possibly be on fire. In the unlikely event that the protected
route is breached, you are required to have a loft zone protected for 30
minutes, long enough for the fire brigade to pluck you from the mandatory
escape window, which must be easily reachable by a ladder.

It is intended that the ladder is provided by emergency services, although a
rope escape ladder can't be a bad idea and I reckon should be mandatory,
really. It could easily fit in a purpose built cupboard fitted in the escape
window soffit.

Christian.