Paid "cash in hand"?

[naters]

Say someone (who is Canadian) I know was employed as an intern the past summer (10-week full-time internship which started 8 months ago with £3750 as monthly stipend as listed on contract) on a Tier 4 student visa, and was not asked for their national insurance number (to their fault and ignorance they had not applied for one). The employer did not ask for it either throughout the internship. Due to amount received being below taxable amount, that someone didn't think much of her pay not being deducted at all, and didn't realise a national insurance amount was supposed to be taken from pay.

That someone received an offer from a major corporate, and finally applied for a national insurance number two weeks ago. However, the corporate who is conducting background check is stumbling across the fact that they do not already have a national insurance number. Have they broken the law? What can be done to rectify the situation? It goes without saying that the person had zero intention to have taken a job to effectively have been paid "cash in hand", i.e. money sent to their bank account.

Thank you in advance

[ULA]

In order to work legitimately within the UK, the individual should have registered with the UK Government for taxation purposes and been issued with a National Insurance number.

However I do believe that there is in place a bilateral agreement on social security arrangements between Canada and the UK which means that an individual does not need to pay National Insurance or have a number. It may be worth the person phoning the Canadian consulate to verify this is the case.