If you only drive a limited number of miles each year inform your first alternative car insurance online of your typical yearly mileage whislt filling in the online form and they may offer you a lower quote.
Some companies now offer child car seat replacement, which means they will replace your child's car seat after an accident even if there is no visible damage.
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.