Stuart,
On the application form for becoming a driving instructor, they ask you for previous convictions during the last 4 years (not 3 years!). Note that even if you don't have any points on your licence, any fixed penalty offences will still be taken into consideration when considering your application. If you have been convicted for drink driving, the endorsement will stay on your licence 11 years from the date of conviction which makes me wonder why you don't have any points on your licence when the conviction was just over 3 years ago?