Actually Tesco need to sort it out. I had this problem when working for an agency and racked up a 400 pound rebate in a few months because the idiots didn't get me to fill out the correct forms when I was registered. The employer should get the employee to fill out a form with relevant details that the employer passes to the tax office, they then know what to charge and tell the employer.
If the tax office do not have the information, they don't know if she has other jobs or any exemptions so defaults to assuming it's a second job for a normal working person and charges the full whack without taking into account the minimum threshold.
Tesco need to submit correct record and she needs to write to the tax people to ask for a refund. After a couple of months she should get a check