what would any Millennium series related thread be without Fred1 bitching about it.... lol
no seriously, it looks like the most cost effective way is to fly to one of the London airports, and drive up to Birmingham.
You get a nice drive around the M25 (the world's biggest parking lot) but once you start headed away from the city, it's a nice drive.
The train idea also sounds promising, however be warned, English trains ain't the fastes things on the planet...
Still it's more comfortable than being jammed into the back of a small rental car...!