Yes and No! Not if they have raised objections to its terms. See implementing contracts (and implied consent) and look at the section changing terms.

Just because you do not have a written contract, this does NOT mean there is not a contract in place. There will be a verbal contract and an employee will have been employed under a (verbal) contract of employment since they started with you. You therefore need to consider and understand the terms of the contract (this is where disputes can arise if the contract is not in writing).

If you are going to dismiss someone, you need to follow the correct procedures.  The employee may have the right to claim unfair dismissal depending on their length of service and reason for dismissal. Also see ending employment and notice periods

It is a legal requirement to provide a written statement of terms (i.e. this is normally the contract of employment) of employment on day 1 of employment. 

In legislation, an employer must give employees a document stating the main conditions of employment when they start work. This is known as a ‘written statement of employment particulars’. There are key terms of employment that need to be given to the employee on their start date and other terms can be given within 2 months. However in practice, the simple way to ensure you meet legal requirements and provide clarity of terms is to issue the employee with their full contract of employment on or before their first day. See the guidance on the written statement for more details.