Technically yes, but it will depend on how you reply to my answer.
If you are going to keep the car at your old address (say for exmaple you don't have a drive or garage at your new address, but you do at the old one), then you can declare that your car is kept there overnight.
If you have no intention of keeping the car at the old address, but at the new address, then I would advise changing your risk address with the insurance.
I understand where you're coming from though - mine went up a stupid amount when moving a few streets away, and I know full well that the level of crime in both areas is the same, but it's all based on the statistics our pricing department are supplied with.
The problem you would face if you kept the car at the new address, but said it was at the old one is if it is stolen or set on fire - your insurers could potentially void your policy for providing false information as to the overnight location of your vehicle!