So happens I just came back from the Canadian F1 Grand Prix a couple weekends ago. Different tracks may have different rules, so please keep that in mind.
Some pointers for you:
We didn't have any issues entering, while proudly displaying our white giants: EF100-400, EF70-200 + 2x, and others in the bag. We also had with us monopods. Generally there's a tripod restriction, at least on race day, so we didn't tempt fate there nor did we care to lug any around.
This will be your best day to capture some great shots. Most people will not be in attendance, so you'll have plenty of room to maneuver and situate on the stand. Feel free to pan those long lenses with little risk of obstruction. Get the monopod out too.
Depending on the location of your grand stand (by popularity), it will be a fair day to shoot. It is likely to get really crowded before F1 qualifying session begins, making you realize just how good you had it the day before. So be ready for that.
Worse day to shoot. For one, you want to actually be watching the race not focusing on shooting. It will be insanely crowded (shoulder to shoulder). Panning shots less likely to pull off, due to the lack of clearance. We had a block of 5 seats reserved, so it was still manageable, but hardly ideal. I would not be comfortable waving the long lens, if sat right next to a stranger, merely out of respect.
I would highly recommend the use of monopod if you are looking to greatly increase your keeper rate for panning shots @ >200mm, although I really despite using one.
I personally used the 100-400 on day 1, 70-200+2x on day 2, and 70-200 on race day. If I had to choose only one, it'd been the 100-400L for the size (collapsible) and weight. The 70-200 (2.8L II) + 2x TC III combo felt like an anvil after a short time free-holding (no monopod). The AF performance and picture quality between the two 400mm setups were very comparable. Clearly the 200mm by itself is superior to either (AF & IQ), but at the expense of the extra reach.
AI-Servo mode is a no brainer for this type of shooting. My preference is to shoot using Zone AF (5th out of the 6 available modes) and set centered. Once locked on, 5D3 would pick up any slacks by actively select any of the 8 adjacent points within the zone. The zone is tight enough to not allowed focus to wonder off the intended subject. Works like a charm! This new AF system is really quite amazing. Even better than the 7D, that I had a while back. 5D2 ... not even in the same league.
I further tweaked the AF configuration as follows:
Tracking sensitivity = -1 (minimizes interference from fences, walls, poles, other cars, and people)
Acceleration/deceleration tracking = 0
AF point auto switching = 0 (minimizes unintended focus shift)
AI-Servo 1st Image Priority = focus biased
AI-Servo 2nd Image Priority = focus biased
You might tweak with them differently to suit your own shooting style.
So that's it for now. Let me know if you have any more questions. Enjoy Silverstone. It is a great track. Hoping Vettel wins!