Possibly. Incapability is one of the potentially fair reasons for dismissal. But first you need to consider whether the employee's ill health amounts to a disability under the terms of the Disability Discrimination Act 1995. If so, you might need to show that your treatment of him was for reasons unconnected to his disability - unless such treatment could be justified because the reasons for it were material to the case, and substantial. The Employment Appeals Tribunal has ruled that prolonged absence because of disability may be treated in the same way as prolonged absence because of sickness, but you would still need to show that the reason for the dismissal could not be removed by a 'reasonable adjustment' to the employee's working conditions - otherwise it is discrimination.
If the employee suffers from long-term ill health, an Employment Tribunal would certainly expect you to do everything you can to keep him on, if necessary including an offer of alternative employment. However, if - after consultation with the employee and a medical investigation - there is no prospect of him returning to work, and you cannot keep the position open indefinitely, you may be able to dismiss on the grounds of 'incapability' - even where, as recent cases before the Court of Appeal and Queen's Bench Division have indicated, the employee is entitled to substantial damages because that incapability has been caused by the employer's own failure to recognise the risk of breakdown caused by stress.
To avoid a successful claim for unfair dismissal, you must be able to show that you acted reasonably in treating the absence as a reason to dismiss, and that you acted fairly before dismissing. Take legal advice before you do anything.