While many employers will generally accept a medical fit note as confirmation of a genuine illness, the medical fit note itself has only limited legal standing. So, for example, if your employer suspects you of malingering, or being fraudulently absent, your employer is not obliged to accept a doctor's certificate at face value.
Your employer may choose to 'look behind' it. If your absences are of long duration or, alternatively, of short duration but frequent, this might impact on your ability to do your job or your organisation's ability to meet its obligations. This might encourage your employer to want to take further action.
The possible implications are that your employer may seek your permission to approach your doctor, or request you see a doctor appointed by your organisation for a report to be prepared on your condition. While you need not consent, if you don’t agree, your employer will be entitled to make a decision about the impact of your health on your ability to do your job on the basis of the information that it already has.
Once your medical condition has been understood, your organisation will need to consider how it can accommodate it. If your level of absence continues to be high with no improvement and your absences affect organisational performance, eventually your employer might lawfully conclude that dismissal is unavoidable.
Therefore, before dismissal becomes an option, you and your employer should discuss ways of minimising the impact on the organisation and whether there are any ways to help you manage your health better. Also, if your illness amounts to a disability under the disability discrimination provisions of the Equality Act 2010, then your employer has a duty to make reasonable adjustments to help you do your job. These could include more flexible working arrangements or moving you to a less strenuous post.
Finally, before dismissing you, your employer must follow a proper disciplinary procedure which allows you the right to be accompanied and to appeal against any decision.