Roland Perry wrote:

There are escalators at Leicester Square - where the line will be
essentially the same depth under the surface. I don't remember the
layout, but presumably there's two flights with a circulating area
between, like at Holborn. That doesn't require the two sets of
escalators to be under one another [1], the unusual arrangement at
Westminster being because of the available footprint for the station I
guess.

The escalator layout at Leicester Square is different to that at
Holborn.

At Holborn the ticket hall is at street level, with a bank of four
escalators down to a concourse. From that concourse access to the
Central line is by a level passageway and short flights of stairs down
to each platform - which are separate and not directly linked by
cross-passages. Access to the Piccadilly line from the concourse is by
another bank of three escalators, then by passageways and stairs going
both down and up depending on platform, because of the unusual history
and unique layout of the Piccadilly line station. Interchange traffic
thus uses the concourse, as there is no other link between the lines.

At Leicester Square the ticket hall is immediately beneath the road
junction, and accessed by stairs, with two banks of three escalators in
a v-angle, each leading to a concourse. Before Angel had escalators,
the Piccadilly line bank at Leicester Square was the longest on the
Underground. Access to each of the lines from the concourses is then by
passageways and stairs. There are further low-level connections between
the two lines, meaning that interchange traffic does not use the
escalators. Both lines have conventional back-to-back inner platforms,
with common staircases.

Westminster's escalator layout is indeed because of the restricted
footprint: almost all passenger access to the Jubilee line is contained
within a huge excavated box with internal structural support, whereas
the other two stations have traditionally excavated escalator shafts.

Covent Garden's platform layout is similar to Leicester Square, and as
it is so close to Leicester Square with similar elevation any escalator
scheme would indeed have very long vertical travel to overcome,
probably requiring surface building relocation for a one-bank scheme.
However, IMO given the layout of the current ticket office it would be
best to relocate it entirely rather than have a two-bank scheme -
otherwise the station would be closed for the duration of the works.

It's difficult to work out what would be the best option if they did
decide to rebuild - perhaps a sub-surface ticket hall immediately to
the north of the market buildings, with several surface entrances
(similar to Leicester Square). Escalators would then lead down in a
northerly direction to a long concourse parallel but above and to the
south of the platform tunnels. From there perhaps three or four new
passageways and staircases down to the platforms, as well as
incorporating the existing two staircases.

One thing is for su it would be a very expensive station rebuild,
for what is essentially existing leisure traffic. There would be more
people using Covent Garden station, but I don't think there would be a
significant number of extra passengers for the Underground overall.