I rotate through antique/classic cars about every 5 years. I buy one in alright condition, slowly fix it up/restore it on weekends until it's in good enough condition to be a daily driver (normal commute is less than 2 miles), drive it for a while, then sell it and use some of the money to buy the next one. They're really not ready for specialized insurance until the last year or two I own them. That being said...because of the distance I drive, and the fact that it's only used for commuting/events/whatever (no out of town trips, not trips to the store, etc.) I typically have it on the super-cheap "I barely drive it" insurance and the company I'm with now (GEICO) has really good rates for antique/show cars.
That's kind of the scenario I was thinking of for the UK, where they have a very limited mileage insurance (2-3k miles per year). Typically owners of these cars only drive them rarely at the weekends, and only in the summer/in dry conditions.