We proposed a cooling-off period which would have seen the unions lift their threat of strike action while we would extend our formal consultation period and continue talks at Acas.
However, the leaderships of the RMT and TSSA continue to threaten strikes. This is despite our commitment that all Tube stations will remain staffed and controlled at all times when services are operating.
In future, there will be more staff in ticket halls and on platforms to help customers buy the right ticket, plan their journeys and to keep them safe and secure.
The confrontation came during the Mayor's monthly phone-in show on LBC 97.3 - thought to be only the second time the two men have spoken.
The dispute over ticket office closures was deadlocked tonight with millions of commuters almost certain to be caught in the crossfire.
London Underground says services will be affected from around 9:30pm on Tuesday 4 February.