It’s a bit late, but the London Midland and SouthEastern train service have both just released a Windows Phone app for their service.

Presumably by the same company, judging from the screen shots, the SouthEastern on track app offers:

Personalised dashboard for your regular journeys

Live departure and arrival boards

Station facilities and parking

View updates for London Underground Tube routes

Submit delay repay claims

The London Midlands on Track in addition lets you:

Customise the app to save and display train times, service updates and platform information for regular journeys you make

Contact customer services

The apps can be found at the links below: