Make sure you have buildings insurance policy in force. Remember though that if you are buying a flat, the landlord or management company probably does the buildings insurance for the whole building.
You should arrange contents insurance to come into force when you move in. It may be cheaper and easier to combine it with the buildings insurance policy.
If you have to set up life insurance to comply with the mortgage offer, you should make sure you do it as early as possible before completion and supply the relevant evidence to your solicitors, who may have to pass it on to the lenders for their approval before they will send out the money.