You can go straight to the new (beta status) custom page by going to www.bbc.co.uk/mobile/betahome/ in Web (there's also a link at the bottom of the standard Mobile home page. Here are some screenshots to give you an idea of how it looks and works.
Here's an extract from the press release, from the BBC:
The BBC today unveils the beta version of its new mobile homepage, which for the first time lets users personalise the BBC content they view on their handsets.
The new mobile site adapts automatically to give the best viewing experience for different handsets and networks.
Mobile users can now choose their favourite parts of the BBC mobile site and arrange the homepage as they wish, expanding or shrinking sections to achieve their ideal mix of music, news, sport, TV and radio, or any other BBC mobile content.
And for the first time, mobile users can localise their preferences for BBC information such as weather forecasts, TV schedules or news stories.
The BBC’s award-winning iPlayer* service fits in neatly too, along with other live schedule information and AV content from across the BBC.
This breakthrough follows the successful revamp of the bbc.co.uk homepage last year and is more evidence of the BBC’s rapid progress in opening up its rich quality content to a fast-growing mobile audience."