And how would you get an escalator anywhere without it hitting the
victoria line running tunnels (if heading east or west) or the northern
line platforms (if heading north)?
This is tricky, yes - i think you couldn't do a direct link to the ticket
hall. Things i can think of:
- Bring the escalators up to the south of the Circle line, and join the
southern end of the shallow-level passageway that runs from the ticket
hall to the Circle platforms, rather than the ticket hall itself. This is
not a great idea: it means changes from the Chelsea-Hackney to the deep
lines involve coming up four levels and then going back down, via the
not-very-large Circle line passageway. I also don't know how this would
work with respect to gatelines.
It would cause huge congestion at one of the most dangerous places for
it - the top of the main escalators.

I'm also not sure how the recent works
have changed the situation in the maps, so this might be totally
implausible. You could do something similar, but instead of joining the
existing passageway, run a second one parallel to it, over the Circle line
and into the ticket hall behind the gateline, but it's still a long
change.
No you couldn't, if you did that you'd hit the fleet river; it runs
under the ring passage where the booking windows are, and then round
under the passage at the top of the steps from the circle line, hence
the reason they kept the five or so steps instead of making the
passage the same level as the rest of the bit behind the gateline.

- Link the Chelsea-Hackney platform to the concourse at the southern end
of the Piccadilly platforms, a one-level change.
Absolutely no room. The Northern line escalators AND the Picadilly
line escalators are both situated there, and its heavily congested at
the best of times; really bad idea. Such a bad idea in fact that they
are already going to close up the side passage with steps from the
victoria line down to there as soon as the northern ticket hall
passages open, because it causes too many problems.

Possibly more escalators could be added here.
How? Its solid escalator round there until you hit the running tunnels
themselves.

- Link the CH platform to the Victoria concourse by similar means.
Threading a two-level escalator up between both the Victoria and
Piccadilly lines might be impossible, though - it looks just about doable
on the map, but i don't know.
Its do-able if you ignore the need for walls, and the structural
support to the tubes, and the passages above them, that walls give.
The space between them is about 10 metres at most, and it really
wouldn't support the weight. Plus it gets narrower as you get closer
to the tube ticket hall until there's zero room left; escalator steps
are fixed width, and don't narrow the higher up you go (and such an
invention would be very dangerous at the top).

- Have an escalator coming up three levels immediately to the south of the
Victoria tunnels, which would finish just above them; from there, a short
passageway crossing over the Victoria tunnels, then another escalator up
to the ticket hall.
The problem here is that there is nowhere for them to meet the ticket
hall at.

The problem here is the Circle line - the first
escalator might need to emerge, er, into it.
Yes, or pass through the fleet river, which is another impossibility.

If there was, this would also be a really easy way to
connect to the Circle line - you have a little concourse underneath the
eastern end of the Circle line station, with steps up and west to the
Circle platforms, and up and north to the ticket hall (through the south
wall).
You could do that of course, but that's somewhat impractical - far too
many steps involved. A new line and its the worst for step free
access?

The combination of the escalator to a sub-Circle concourse, with steps up
to the Circle platforms and ticket hall, and the steps up to the
Piccadilly concourse would give you a pretty direct route to all the other
LU platforms and the ticket hall.
Sub circle is fine for circle line interchange and exit, but its
absolutely rubbish for interchange with any of the other lines - all
the way up, then up some steps, then down some steps, and down more
escalators? I'm also thinking congestion.

Its further than the end of the victoria line - the connecting tunnels
are very long, and only just reach the far end of the KX thameslink
platforms.
The *far* end? I'm afraid i've never been down there (and now never will)
- do you mean the end nearest KX, or furthest from it?
I mean the end nearest KX, the western end of the thameslink
platforms. The eastern end is even further away. The whole of the KX
thameslink platforms are very far away from the rest of the station

But if you dig through the south wall, there's enough room before the
Circle line to accommodate a new escalator heading east, beside the
Victoria escalator. Or some steps down to a concourse beneath the Circle
platforms, as i mention above.
South wall of what? There's a river behind the south wall of the tube
ticket hall. And there are tube running tunnels to cross first at the
south wall of everything else.

perhaps the Circle platforms, at the western end.
The problem with that is that the only way it can go is south or north
from those platforms, because directly underneath them, and to the east
and west of underneath as well, is the victoria line running tunnel.
AIUI, not quite - the Victoria tunnels are a touch to the north. Steps
down from the Circle line platforms (not sure where you'd put them - at
the east end, on either side of the steps going up?) would miss the
Victoria tunnels.
You could do it with some awkward steps, but they would be very
awkward, and far too many steps (since you have to add on the steps to
get to the circle line in the first place). And you still need two
different exits to comply with Health & Safety.

I've always wondered why they never built the victoria line platforms
there instead - it would have allowed better connections to the other
lines - perhaps there's an additional obstruction around there as well.
It looks like the Victoria tubes curve northwards west of the platforms;
if they didn't want the platforms to be curved, they'd have had to bulge
out more to the south of King's Cross, which maybe they didn't want - as
you, say, maybe there's an obstruction.
They head towards Euston, just like the circle line and northern line.
I'm not sure why they might look like they curve in that diagram, its
probably just an illusion due to the two running tunnels approaching
each other, after being far apart to fit the platforms in.

You'd widen the concourse at the foot of the escalators, so that people
could walk round them, on to a set of steps going down. There's just about
room for this.
There's a great big hole on the northern side (not shown your map),
and you'd need to go quite far around them if you wanted to make sure
there was enough wall between the escalators and you to ensure
structural integrity of the tunnels above you.

Take a look at westminster jubilee line and look at how absolutely
huge the space taken up by escalators is; well you need that much
space plus a lot more to provide wall support to hold up the ground
above.

The Piccadilly platforms are even worse - they have escalators to the
ticket hall AND the northern line at that end - the congestion there is
already atrocious, so even if you managed to find a gnats breadth in
which to place the escalators to the chelsea-hackney you'd jam the
entire station due to the congestion.
I agree that it would be unwise to make this the only route up from the
CH. It would be a useful way to do interchange,
No, it really wouldn't. There's already a narrow interchange passage
there to the victoria line, and they want to block it up because it
causes such bad congestion with the piccadilly and northern line
access - imagine how much worse it would be if it was a proper
interchange connection.

The major advances in civilization are processes that all but wreck the
societies in which they occur. -- Alfred North Whitehead
Like Solon?
Like everything from the invention of agriculture through to the extension
of the East London Line!
Solon invented democracy.