In that we are only talking about an access point, what's the problem with
an escalator down-and-up, or a moving walkway underground, between Leicester
Square and Covent Garden?

There's plenty of space in the Square itself for a new access point.

Please submit draft plans, with due consideration of other sub-level
constructions and approximate costings.

Also price up a publicity campaign designed to remind travelers that
there are alternative convenient routes.