No tax or NI is payable at £130pw. However at this level (above £107pw), the employer should be registered for PAYE and reporting your earnings because as others have mentioned you earn National Insurance credits towards the basic state pension, as well as jobseekers allowance and other benefits.
You should receive a payslip each week, and it is normal (although not mandatory) to show your National Insurance number on the payslip. Has your employer asked you for your NI number?
No I thought not. They are breaking the law.
Do you have a written contract? Or a written Statement of Employment Particulars? No I thought not - they are breaking the law.
What paid holidays are you entitled to? Is it at least 5.6 weeks (although 1.6 weeks of these can be bank holidays)? They may be breaking the law.
Breaking the law regarding employment is a form of exploitation. Paying £130 plus board and lodging for 50 hours work is also a form of exploitation, even if it is your first job and you are young (I presume you are at least 18, and that the 50 hours is full-on work and not just babysitting while kids are in bed).
Now for practical things - do you have a National Insurance number? What nationality are you?