Health officials said two other cases were potentially linked to White Post Farm, which "had different strains of E.coli 0157".
Doctor explains E.coli
In a statement, the health protection agency (HPA) said: "There are many potential sources of E.coli and as yet there is no confirmation that the farm is the source of infection in these cases, all of whom are well."
Animals at the farm are being tested over the weekend and the farm will stay shut until the results are known.
E.coli can live in your body for up to two weeks, so there is a chance that many more people could have it.
E.coli causes vomiting and diarrhoea and, in very rare cases, can kill people.