Dawes Kalahari, Puch Prima Super Sport, Graham Weigh 853
The deciding factor is usually the frame and forks. If you can't fit pretty wide tyres, the bike couldn't really be called a cyclocross bike. However, this does not mean that you cannot use it for riding dirt roads and cycling paths. You can do that just fine with narrow road tyres. But you would be better off fitting the widest slick tyres that fit between your forks/rear stays/brakes. You should be able to at least get 700*25c tyres in, maybe even 700*28c.