Have 6+ Points or Driving Ban?

For car, van and bike.

Get a vehicle with a low insurance group rating. This will not only keep your cost lower but it could also mean that more insurers will be willing to offer a quote. A high group vehicle puts the cost up even more and will restrict the number of companies who will quote.
Avoid modifications to the vehicle. All mods must be delcared to the insurer and will only push the price up. Try to buy a standard fitted model.
Do an advanced driving course. Many insurers offer a discount for passing the course and you may find that more companies are willing to offer you a quote even though you have convictions.
Reduce the number of miles you do. The less time you are on the road, the less chance you have of being in an accident. This could reflect in lower rates.