If an employee is not performing well at work then you are entitled to dismiss them.
An essential ingredient required to make such a dismissal fair, however, is to follow a proper dismissal process. As an employer you would need to have a good reason to dismiss a member of staff on performance grounds, but if you fail to carry out a fair procedure, your employee may have a claim for unfair dismissal.
Under the ACAS Code of Practice, if you as an employer have concerns about the performance of a member of staff, then you should inform the employee of your concerns and give them the opportunity to improve, as well as provide support and assistance in allowing them to do so. An employee should be provided with a number of warnings (usually, verbal, followed by one written and one final).
If there are objectives to be set, these need to be made clear to the employee and they should not be unachievable.
If a performance programme is coupled with disciplinary proceedings where they could be dismissed, then they should be informed in writing of this in advance.