HMRC told me to do an unemployed tax claim in september when im actually employed

So long story short. I worked at a place for two weeks then left. I was on emergency tax code. Half my salary went into tax. to get the tax back I need to ask for details of my current employer. Turns out im not even registered on HMRC as an employer/ idont receive payslips either. They told me to write a letter in saying this and tell them that my current employer doesn't have details etc. I called in today to ask questions and the woman said In September I can just do an unemployed tax claim but isn't that lying and illegal as I am technically employed its just not registered under HMRC. I don't want to get in trouble for lying etc.
was she encouraging me to do something illegal or what?

your current work is paying you cash in hand then?

nope I receive it directly into my bank account

but no payslip at all to show that they're paying tax on that? i don't think hmrc were encouraging you to do something illegal but i do think your employer could be by not giving you a payslip

i dont pay any tax for the job as im a student. So its fine if i do unemployed tax claim?

i dont pay any tax for the job as im a student. So its fine if i do unemployed tax claim?