That depends on your location - in the UK, like the OP, the vast majority of cheese is made with fungi / bacterial alternatives to rennet - over 90% of cheese is vegetarian friendly, including most cheeses used in the catering industry (Parmesan and a couple of other exceptions apply). There are widely available alternatives to those cheese which for their own reasons do use rennet (e.g. you can buy a veggie parmesan-type cheese, as true Parmesan is DOC and made to strict regulations)