If you hollowed out
the existing station and put in a downward-sloping track at a gradient of
1:30 (generally considered the practical maximum, i think), you could drop
But if you did that, you wouldn't have Cannon Street Station, meaning
that the Commuters all pile off the trains at whatever the next
station is - presumably Bank, which would be a disaster in terms of
how busy that station is already.

You might need to demolish No 1 Poultry, but it's a horrible building anyway.
Its not such a problem - the bottom 2 floors worth of basement are
isolated from the rest of the building with a concrete slab in between
- they did that so that archaeologists could get down there while they
were building the building above them. But, if you were heading in
that direction, you'd run straight into the Waterloo & City line
platforms, travelator, or the passenger tunnel between the Waterloo &
City platforms and the Central Line.

Don't ask me about how it all fits in with the Bank station complex.
Didn't someone say they thought that was plausible?
It's only really possible if you rebuild the waterloo and city line
platform entrances so that they take a different route; the travelator
and the interchange tunnel effectively block the through-route - the
only way to avoid this is to go below this level, but then you would
need a very steep slope indeed. You can't get through on the right
hand side of the northern line either, because that's where the
Central line platforms and escalator are.

When DLR extensions have been suggested in the past it is usually
mentioned that the Bank of England vaults are in the way too!
The vaults thing is a red herring when it comes to the NCL, though - there
have been serious proposals from the time it opened up to the 1960s to
extend it southward, and none of those had any problem with vaults.
(from the north) I'd assume it would be fine until you actually reach
Bank station - at that point, if you turn right, you hit the (former)
Midland Bank HQ (now some other bank's important building) vaults,
unless you make it a 45 degree turn. The alternative is to pass
through the slight gap between the central line and the ticket hall,
over the northern line, and then turn right. You can't really head
straight on, because there are loads of vaults around there. The DLR
platforms are to the west of the Northern line ones, rather than
directly below, presumably to help avoid undermining them, or the
buildings above - anything any higher would thus need to be to the
east, which basically means you end up heading more towards Monument,
not Cannon street, and there are quite a few listed churches in that
direction, as well as office vaults, that you wouldn't want to
interfere with.