I researched this for a customer about a month ago :-)
Trains
http://www.londonmidland.com/ (from London to Northampton)
The rail station is about 1.25 kilometres from the Greyfriars Coach Station ( see below)
Coach
http://www.nationalexpress.com/ (from London to Northampton)
You can actually get a coach from many places in London to travel to Northampton. They appear to go at regular intervals so that is not a problem.
You would arrive at the Greyfriars Coach Station in Northampton
http://www.stagecoachbus.com (from Northampton to Silverstone)
From this bus station there is the 8 or 89 bus which travels through Silverstone. I can’t attach the timetable but you can download it from their website as an adobe pdf file. The buses run Monday – Saturday only ie not on race day.
Also, if you go to Silverstone’s site
http://www.silverstone.co.uk/events/2012-Formula-1-Santander-British-Grand-Prix/
and click on the “Getting to Silverstone” link (3rd para), it says that Stagecoach Bus company “will be providing a Grand Prix bus service to and from Northampton train station on all days of the event.” Unfortunately the specific link to their website is out of date.
I hope this helps.
You will certainly have options either by train/coach or just by coach
Please check all this yourself though! :-)
I would be very interested to hear if anyone else has other suggestions