Nope. None of the cover I ever looked at includes third parties. I would be amazed if it did as the very nature of being on track puts you into close company with people of hugely varying experience and ability. If people start racing and trying to outbrake people then the risk of an incident increases massively. These things are not supposed to happen on track days but I can assure you there is always at least one who thinks the rules don't apply to them. Fortunatley Mandy and co have clamped down on this.
The cover is only to protect you from something you do like losing control and hitting a barrier. Note that depending on your cars value, this is also where there is no guarantee the insurance is worthwhile. When I last looked at this, the cover for my GTS was about £600. As it was then valued at £80K, the excess was £8000 as it was 10% of the value. My view was that while there was always the possibility of having a major accident that did major damage or even wrote the car off, that bad day was going to cost me at least £8600. If I only had minor damage up to £8000 in value, I was paying for that anyway and had just given the insurance company a £600 for the privilage of being insured.
I have not looked into the policies like Lockton offer that include free track insurance for PCGB track days. The insurance costs more anyway but if you did several track days it might pay off at least in comparison to one off premiums. I doubt that the basic cover is any different.
Trust me if I thought there was a cost effective way to protect my pride and joy I would take it. When you apply to places like Adrian Flux they ask for experience. I have race experience and multiple track experience on two wheels and four. Seems to count for very little as I am going on track along with people who potentially have none and also with a range of cars of varying performance.
So insurance is a personal choice. On a track day I am there to have some fun and get my 'fix'. I will go around Goodwood in about 1.30, and Donington in 1.21 and thats fine for me. I'm not trying to set any records or win a race. Enjoy it and drive home