If your van does not have an approved immobiliser fitted compare prices for vans that have fitted and unfitted. It might be cheaper to have one fitted than pay a higher premium.
If you belong to a professional body or a trade union check to see if they negotiate cheaper van insurance for their members.
Any penalty points you have previously accumulated must be declared to your new insurance company.
Making a claim will not automatically lose you your no claims bonus. Most insurers will relegate you only two years meaning if you had 5 years no claims then you would still have 3 years.