Starting disciplinary proceedings against employee on certified sickness

I would appreciate some thoughts from the wise heads on here. What can be done if it is believed a member of staff has obtained certified sickness absence in order to avoid disciplinary actions for serious misconduct? 

We have a member of staff who was going to be subject of disciplinary proceedings but was on holiday when the offences came to light. 

The lady in question has had multiple unauthorised absences that clearly demonstrate it was repeated and habitual behaviour on her part.  None of these absences were ever mentioned to any of the appropriate managers and she has not followed the Sickness and Absence Policy to account for any of the absences.  The nature of her role means that it was easy for her to not be on site to perform her duties for all her working hours and it was not possible for those duties to be performed from elsewhere.  Almost all of these absences were of the nature of leaving work several hours early or of taking very long lunch breaks.

There is clear evidence of her behaviour and it is deemed to be sufficiently serious to lead to instant dismissal unless she can provide a very good reason for her repeated absences, especially in light of the fact that she has never advised any of the management team of any of the absences or of any issues that would affect her ability to perform the role as required.

However, there is a suspicion that the investigation has alerted one of her colleagues who has tipped her off and she is now using the certified illness as a shield against the disciplinary action.  She has not been provided with any notification of the company’s intent at this stage but the Doctor’s Note already provides for several weeks off and we feel it could potentially be longer than that due to the nature of the condition.

What we would like to do is begin the process now.  We are a fairly small company and need to resolve this issue and if necessary recruit a replacement.  Can we safely push on with the disciplinary process in these circumstances or do we need to wait until she returns from her sickness before instigating the action?  Is it legally safe for us to conduct the disciplinary process in her absence and even dismiss her?  We want to be fair bout this but the evidence is very clear that she has been caught “bang to rights”.  However, we want to give her the opportunity to provide her side of the story but if she refuses to co-operate we can’t afford to allow this situation to drag on for months.