Surely there can be a contract if there is nothing in writing?
Yes there can. A verbal contract (particularly where the employee has already done some work in return for pay) will be equally binding — though it may be more difficult to prove what the precise terms of the contract are (see question one, above). As well as providing the legally required written statement, make sure that you have written evidence of any other important contract terms. Do not leave things to chance, or you might regret it.