Any given autocross event will see all manner of cars. All you need is to pass a safety inspection and have ~$25 and you can run. We'll see anything from vintage muscle cars to a Honda Fit on track. Triumphs, Minis, Sunbeams, MGs, and Lotuses (or is it Loti?) are regular attendees. Many regional sites will still have results posted for last year. You can see what people drove at each race there. It's all in the name of fun and this is what those little British cars were born for. If you are worried about "Competing" there is a vintage class for you. You'll meet some great people and at the very least will see a great car show.
Hope to see you out there. I'll be the guy in the Miata pictured to the left.