You'll find a big difference in the cost of home insurance. Normally policies put forward by lenders will be relatively expensive for buyers in terms of insurance premiums.
Lenders may also look for you to insure your life to at least the value of your loan so that should you die the loan will be repaid in full by your policy. You'll need to have the paperwork to prove cover exists.
In the case of ordinary repayment mortgages, lenders may insist on the borrower(s) taking out a mortgage protection policy to cover the amount of the loan. Such a policy guarantees repayment of the balance outstanding on the mortgage in the event of the borrower's death.
It's worthwhile looking at contents insurance. Be sure your policy covers the contents while you're moving house. Remember to transfer the policy to your new address at the right time.