Driver SOS (UK)
Helping with car insurance, driving bans, learning to drive and other motoring issuesJoin Community
Can I become a driving instructor even if I have driving convictions?
Your best bet is to contact the Driving Standards Agency to discuss your case. They will surely take into account your driving convictions but as you mentioned above, this happened like 6 years ago and if you have been a "good driver" since then, there's no reason why they wouldn't let you become a driving instructor.
Good luck and if you receive a good feedback from them, let me know how you get on with the driving instructor training.