I researched this for a customer about a month ago :-)
http://www.londonmidland.com/ (from London to Northampton)
The rail station is about 1.25 kilometres from the Greyfriars Coach Station ( see below)
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
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 Unfortunately the specific link to their website is out of date.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