The bank, which acts as the country's regulator for the insurance sector, criticised the policies of charging customers higher premiums relative to expected costs the longer they remain with an insurance provider, a policy known as "price walking."
"Our analysis shows that some of the practices identified could result in unfair outcomes for some consumers in the private car and home insurance markets," the bank said in a report that looked at 11 providers and surveyed 5,500 consumers.
"As a consequence of these practices, the premiums paid by certain policyholders deviate significantly from the expected costs of the policy to the insurer," the report said.
The bank called for a ban on "price walking" in personal motor and home insurance markets, new requirements for providers to review their pricing policies and processes annually and new consumer consent and disclosure rules.
(Reporting by Conor Humphries; Editing by Bernadette Baum)