I'm limited by the information I have but I will tell you what your friend needs to do. I cannot tell her whether HMRC are right or wrong as I don't have any documentation and information is everything in tax.
You said that HMRC appear to think your friend is self-employed. A letter addressed to HMRC from ASDA confirming that she is employed will deal with that and, if the tax that appears to be owed is due to that misunderstanding, it should go away. Having said that, your friend appears to earn below the personal allowance so there would appear to be no chance of a tax liability in any event. The personal allowance level was £8,105 in 2012/13. There are two possibilities I can think of based on what you have told me:
1 HMRC say she is self-employed and may be sending her demands for payment of Class 2 National Insurance Contributions which is a flat rate contribution for the self-employed. For 2012/13, it was £2.65 per week and it is currently £2.75 per week.
2 The demands are for repayment of overpaid tax credits.
Your friend needs to check her status with ASDA and get them to write a letter as I explained above. Does she not have payslips from ASDA? Did she get a P60 for 2013/14 in April 2014 and for 2012/13 in April 2013? If she has these documents, she should call the tax office on the number here
and thrash it out with HMRC. She needs to find out what type of tax is being pursued, income tax, tax credits or NIC or any other. The letters should tell her what HMRC want her to pay.
If she appears to be getting nowhere she should activate the complaints process which you can read about here
. That will lead to a more senior official at HMRC looking in detail at your friend's situation and should resolve it one way or the other.
If your friend is not confident enough to talk to the tax office herself, she might get you to help her by calling the tax office, passing security to confirm her identity and then passing the phone to you to ask questions. Alternatively, she could visit the Citizen's Advice Bureau who will call the tax office if she has all her paperwork with her.
I'd be happy to look at any documents if you can upload them but, in the meantime, I hope what I've told you gives you a place to start. Your friend will get nowhere by letting the matter fester.