You need to be aware of advice given here concerning points and convictions. The two are entirely separate for the your purposes.
The penalty point system is designed to enable courts to disqualify drivers who commit a series (between two and four) of minor offences, any one of which would not normally attract a ban on its own. However, it is possible to be convicted of an offence and receive no penalty points. Points are not imposed for any offence which, by itself, attracts an immediate ban. Nor are they imposed for each individual offence when a driver is convicted of a number of matters which arise from the same incident. (For example, if a driver is convicted of no licence and no insurance he will receive points only for the most serious – no insurance).
In these circumstances, his licence is “endorsed” with the conviction details. These details remain on his driving record for either four or eleven years (depending on the offence). When applying for insurance the usual questions are not “do you have any points?” but more likely “have you received any convictions in the last x years?” The number of years for which details are requested varies between the companies, but it is now often five (or ten for drink and drug related offences). So even though he may have no active penalty points, the driver must disclose the convictions or risk having his insurance invalidated.