London Heathrow to Birmingham
 

What is the best way to make that travel. My flight arrives at 12:40pm...can't find anything on the web...

If you take bus(every 1/2 hour to 1 hour) from Heathrow to Reading(about 45 minutes), there are frequent train direct to Birmingham(1 hour and 40 minutes). For train timetable and fares, please check: thetrainline.com.

do you know how far it would be from heathrow to euston station?

If you take Heathrow Express (15 minutes-20 Minutes) to Paddington Station,then taxi (15 -20 minutes) to Euston; or Piccadilly Line from Heathrow to Lesicester Square (45-50 minutes),change Northern Line to Euston(10 minutes).

Hello,

If you want to take the train, I would recommend getting to Marlylebone Station, as you can get a train to Birmingham.

Yes it's weird that there's no direct bus at that time. But by the time you've hiked it to Paddington, Euston or Reading (or Marylebone if you want to go cheaper and slower), and waited for the connection, you'll have saved no time over waiting for the direct bus at 3pm (do you really think the plane will be on time and you won't have to queue at Immigration?)
In the unlikely event of your really having two hours to kill, go to the chapel next door to the bus station at Heathrow and give thanks for a miracle. Or look at the BAA site for the food and shopping options at Heathrow (Harry Ramsden's - before security at T3 - claims to be the world's best fish + chip place. Try Noon's for Britain's real national cuisine (Indian)

I agree with the poster who said you should get a coach. www.gobycoach.com will help you. You needn't book ahead. Yes, it will take longer journey-wise, but why schlep all the way into town via Tube/rail/taxi etc to get the trian. You'll end up paying a lot and not really getting to Birmingham any earlier.

Check the National Rail Web site and look at First Great Western.
http://www.nationalrail.co.uk/

I travelled that way from Paddington to Worcester, but they also go to some Birmingham stations. And Paddington is easy with the Heathrow Express.

The First GW train was terrific -- very modern carriages, like Eurostar. A fast and comfortable service, and it seemed cheaper than the SW trains I usually take. (On the trip back to London, I was on a Chilterns line train -- much more plebeian. But it still got me where I needed to go.)

For the benefit of future searchers, I should have given the "official" answer to the original post.
There's a bus every half hour to Watford Junction railway station (usually a 40 mins journey) and hourly direct (80 mins journey) trains to Bham, with several trains in between the hour that take about the same time, but require (almost) painless changes.
Virgin Trains' Watford-Birmingham service is reasonably reliable: their Reading- Birmingham service is hoplessly unreliable (about the worst in the country). There are virtually no direct trains from Paddington to Birmingham (actually I think there are about two a day): you have to change at Reading onto the hopeless Virgin service.
The Watford connection is normally faster than the direct bus, though