Some companies pay full pay during sickness absences and it is not unusual for them to include a clause that enables them to refuse to pay if the employee’s accident results from them engaging in dangerous sports outside of work or they may seek to claw back payments from 3rd party insurance settlements. It does seem harsh to dismiss an employee who has, perhaps through no fault of their own, been involved in an accident especially if the financial liability from the company’s perspective is only SSP; however I understand that it may also cause you difficulties in terms of covering her work during her absence.
In which case, if the employee is not suffering from a disability and if there is nothing in her contract to prevent you dismissing her now, and if there are no other factors at play which may amount to discrimination or unfair dismissal then you could let her go on grounds that she was unsuitable for the post because as you say, she is a new starter and would not ordinarily have unfair dismissal rights. Please note that I have included a lot of ‘ifs’ in that answer so it would be advisable to get an employment lawyer to look at the particular facts of the case before you end her employment.
Employment Law Essentials UK 