Diamond and Admiral are the same firm. (Diamond Insurance is a trading name of EUI Ltd, which is part of Admiral Group plc).
Those quotes seem reasonable (in view of the accidents) but it could still be worth trying ALL of the main price comparison websites. Further, it might be worth phoning Post Office Insurance to see what they can offer (0800 783 3770, 0800-2100 weekdays, 0900-1700 Sat, 1000-1400 Sun). I allowed them to call me with a quote in return for being entered into a draw (when I taxed my car at a post office). I wasn't expecting them to beat my existing (carefully researched) premium but they found me insurance at a far lower price.
Chris