Righto let me help clarify a few things.. Now this is my thoughts based on it being one of our circuits and our insurances and personal experience.
Cars are not scrutineered on track days, so fire extinguishers aren't necessary although obviously we would recommend they are there for your safety, but if you have a system ideally it must comply with BS4123 and the pin is in the armed position prior to entering the pit lane, but i have seen many cars with a normal fire extinguisher like the one A2ON197 is suggesting, secured safely in reach of the driver!
As Stuart says, there will always be the gents on fire trucks if ever required, they will be there before you can worry about it anyway!
Gloves and safety wear are advisory but again not compulsory, although i cant think of a reason not to wear any of it.
Helmets, we have a minimum standard (loosely speaking), but again these are not checked either, and i know at Snetterton we hire them out to people should there be an issue. (It is a recommendation to have a Snell 2005 onwards helmet) Obviously open faced in open cars is a no no.
License checking, I have spoken with people at Cadwell this morning to confirm for you all and the credit card part is fine, as it is at Snetterton always. Again, its a recommendation to have both, but the card part is spot on

Obviously as it is an OpenTrack day, they themselves may have requirements they would like met for the day, and as they are the TDO for the day, hiring the facility, it would be down to them to enforce anything on the day they choose to put in place!! They have had very smooth days at Snetterton in the past, with no issues involving any of the above in the past so i doubt there will be any at Cadwell. They are a great TDO and put a lot of time and effort in to making the day run smoothly for you all.
Have fun!!
HTH
J