I'm pretty sure that you need to present a valid driver's licence at any trackday, whether circuit or airfield (because it's an organised day). However, it would be worth checking with the organisers themselves. I would suggest an honest email to either Jonny Leroux at Bookatrack or Marcus at EasyTrack (both websites are .co.uk). Both will be very helpful, and keen to find a way to take your money if at all possible. I think you know the answer, but worth a punt.
There is another possibility. Have you considered private hire? Brands Hatch may be beyond your means, but you could consider the smaller venues like sprint tracks. Perhaps:
- Curborough: Near Lichfield. About £300 for a full day, up to 10 cars (so find a few mates). Small and tight, but it does have a loop that you can keep circulating. Only one vehicle on track at a time.
- Llandow: Near Swansea. About £100 a head, if you mix with others. More open and faster, though still quite short (35 sec lap). Up to 6 cars on track. However, sweet talk them, be flexible, and you will find a day when there are only a couple of others there (and you'll get loads of empty track time)
I've never been asked for my licence at Curborough. I can't remember at Llandow, but I do know they will be flexible (last time I was there, a 14 year old was planning a first run in an FFord). Both have websites (probably .co.uk, but Google will find them)
Sure, you'll get no Paddock Hill or Cascades, but in your situation I guess something is better than nothing. You might also be able to take both car and bike. So arrange a vehicle, chauffeur, and some mates to make a day of it. I think you'll find a good way to scratch your itch.