Hello, I am a solicitor with 20 years experience. I will try to help you with this.
You will have to plead guilty to this. Driving without insurance is effectively a strict liability offence, the only defence being if you reasonably believed that an employer had you on their insurance. These circumstances do amount to good mitigation. Do you have any points on your licence?
no, never had any offences
i thought that i do have insurance
That is not a defence .
Is there any chance of pleading guilty and getting off the points, as it was an honest mistake
No you will not be able to avoid 6 points which is the mandatory number of points for the offence but you should avoid a driving ban -assuming yu have a clean driving record. A ban is unlikely on these facts but if you want to have extra assurance that this will not happen it might make sense to instruct a solicitor to represent you (cost I would guess £250-500). Getting written character reference from respectable types who can write a letter to the court saying what an upstanding law abiding person you are and how surprised they are to hear about the case would also be helpful.