A zoom, and the longer the better, no doubt about it. I use the 80-250 at an oval track (
Tipperary motor speedway.) and often wish for something up to 400mm although that would bring another set of problems altogether. All the pictures on this site are taken with a K10 or K5 (bar one) using either the 80 - 200 or 60 - 250mm
Having said that as you can't get particularly close to the action at Silverstone a fixed telephoto will probably do as you will not be varying the distance between yourself and the subject to any great degree. Speed of focussing is not a problem as you can pre focus and I have found with the K5 shooting on tracking mode can lead to dramatic over exposure when chasing a subject anyway. The attached picture was taken with the K10 and 50 - 200mm from about 15 metres, the bike would be doing 60 mph through this bend so many things are possible without great expense.
One thing is for sure, you'll probably take several dozen shots before they start to come right, timing is of the essence and TBH you are better off taking well timed single frames rather than relying on machine gunning a car as then you are just falling back on luck rather than judgement. Anticipation is the key here.
Good luck with it all, enjoy Silverstone and remember there are also some beautiful villages built of the warm Northamptonshire sandstone in the area that are well worth exploring with a camera. I used to live just 12 miles from the circuit but never got to the see a race there!