I wanted to show my gratitude to this forum members and admins as it has been of a great help through my immigration journey, therefore I'd like to share my recent experience in case it might help anyone in the future.
I applied to change employer via a premium service, and I had the following concerns:
1. I had one criminal convection which is resulted by not responding to a fine related to keeping a car uninsured on the road (letters were sent to old address hence why).
2. I had one FPN which is driving without insurance (fine + 6 points).
I was very concerned that this might attract a refusal on the basis of character,conduct..etc.
I've declared both offences in the application and set out details in the covering letter,provided courts documents and fine receipts, provided character reference letters from my previous sponsors, and also paid a solicitor to write a covering letter explaining the circumstances around the issue, and the demonstrating that a criminal conviction would have never happened if I received the fine letter in the first place.
Also talked about how I took responsibility of my actions and reacted in the best possible way to rectify the mistake.
The result: I was granted the visa within three hours in the same day

Documents provided:
1. Passport, 2 photos, BRP card & documents checklist.
2. Solicitor Covering letter.
3. Previous employer character reference letter.
4. Courts documents, Fine receipts, P60 forms (just to prove I'm a good guy), and even Tenancy agreement (to show that I've moved addresses).
Advices:
1. Don't worry too much I know it's very stressful, but just do the right thing and declare your offences.
2. Make sure your car is insured even if it's off the road beyond use, or otherwise declare it SORN asap.
Hope you find this helpful and wish you all the best,
