So why is cheese not necessarily a vegetarian product?
To make cheese milk has to be separated into curds and whey which requires the addition of rennet. Rennet contains the enzyme chymosin and is traditionally sourced from the stomach lining of unweaned young animals; this enzyme helps them digest their mother's milk. In cheesemaking, that same enzyme breaks down the protein chains in liquid milk. Generally speaking, cow milk cheeses use calf rennet, goat cheeses use kid rennet and sheep cheese uses lamb rennet. Rennet usually comes in powder or liquid form and an incredibly small amount is used to coagulate a very large amount of milk. Vegetarian cheeses are coagulated with either a synthetic rennet derived from mould or yeast, or with a plant derived rennet which would typically come from the cardoon thistle plant.
There are some cheeses which have to be made using an animal rennet in order to retain their name, e.g. Parmesan. Many British cheeses are made with vegetarian rennet but there is no hard and fast rule as to which cheeses are suitable for vegetarians and which aren't. Some cheddars are vegetarian, some are not... Many vegetarians eat all cheeses as the amount of animal rennet used is so small but if you want to know which cheeses are completely vegetarian then the staff in the shop will be able to advise you.
Vegan cheese is a whole other topic and at present we don't stock any vegan cheeses.