What the law requires you to do within two months of starting an employee is to provide a written statement of terms and conditions of employment (Employment Rights Act 1996) - that should be distinguished from a contract of employment which is the nature of the relationship between you and the employee.
Why is that important? Because it means that you can add, with the employee's agreement, pretty much anything you remember as time goes by by way of separate agreements in areas such as restrictive covenants and working time changes and, and I'm not saying this is a good thing, you can terminate the contract with statutory notice at any time in the first year without the prospect of a tribunal (discrimination excepted, obviously).