It appears that from today, London Underground are starting a trial of Wi-Fi, which will cover both the station and the platforms. Before you get too excited, firstly it’s only one station (Charing Cross Station), and it’s not free either (being part of the chargeable BT OpenZone system).
Having said that, it will offer free travel updates to all Wi-Fi users, and of course, many users (most but not all BT Broadband customers, and manyowners) have some inclusive OpenZone minutes as part of their contract, so it will be very useful for many.
The trial will last 6 months, although it’s likely to expand (in my opinion) and become a key feature across multiple stations. There are no plans for coverage within the tunnels.
More details on the TfL website. Picture (c) Transport for London 2005.