If she has only been there for 6 months she can't claim unfair dismissal (only constructive if you resign) unless its one of the discrimination headings such as race, sex, disability, religion or sexual orientation, age etc.
it would still be good practice (but not necessary under law) to follow the 3 step statutory dismissal procedure. Its very easy for companies to get rid of people like this but at least they have paid her notice and waived the fee.
I think lowfatmilkshakes suggestion for a reason would cover it - change to dept structure