If you are involved in an accident with an uninsured driver you should take their details, car registration and model and contact the police immediately.
For a small extra premium most companies let you protect your no claims discount. However you need to check to see if this is transferable to another aa cheap lady car insurance if you choose to move company at a later date.
Even if you find a cheaper quote than your existing insurance it's worthwhile telling your existing insurers to see if they will match or better the offer. You may find however that online quotes could be the cheapest.