If he was banned because he didn't have a valid driving licence (ie a full uk licence), then he must have been issued with a conviction code of LC20 which would stay on his provisional licence for 4 years from the date of the offence. This means that after 4 years, you can request the DVLA to remove the endorsement and penalty points from your licence. When filling out forms for car insurance purposes, usually you are asked whether you have any conviction for the previous 5 years and if your boyfriend committed that 'driving without licence' offence 10 years ago, then you wouldn't need to put this down.
A more convenient insurance policy for your boyfriend would be a learner driver insurance one which is short term in nature and ideal for what you're looking to do. You will be able to teach him to drive privately rather than spending loads of money with driving schools.