Thanks for your question and for asking for me, and apologies that I was not online earlier.
Its very unusual to say that least that only National Insurance is deducted and not just as well, and as a self employed individual neither should have been deducted.
Usually what would happen is, with self employment, is that all work you undertake is paid gross (without any deductions) You then register with HMRC the fact you are self employed and will pay Class 2 National Insurance, either by monthly direct debit OR quarterly bill - and this costs £2.70 a week.
You then after each 5th April complete a self assessment tax return, declaring all self employment income and all expenses incurred, and any other income (such as employment, rental income investment income etc and HMRC calculate
1) The tax you owe
2) Any Class 4 National Insurance due on self employment only
Which then is paid to them the following 31st January following the tax year in question.
I would have understood is tax had been deducted only, or both (as some jobs might see you being treated as an employee (in which case you would declare this as employment within the self assessment tax return, but never solely National Insurance,
I would approach the company for whom you undertook this work, and establish with them why this deduction was made, as you will pay any National Insurance due under the regime of self employment.
They should either
1) refund this back to you - if deducted in error OR
2) confirm this was employment - and then advise why no tax was deducted.
Do feel free to ask any follow up questions