Bluefin Insurance has found itself in shallow water this morning, as the Financial Conduct Authority (FCA) slapped it with a £4.02m fine for misleading customers.The weighty insurance broker, which was wholly owned by Axa UK during the time in question, was accused by the FCA of trumpeting itself as "truly independent".But the watchdog found that conflicts arose from Bluefin's ownership, as the business had a "culture which promoted business strategies - including a policy which focused on increasing the business placed with its parent company - over treating customers fairly".Read more: No more deals: Axa to decline future acquisitions after blasting through the €100bn barrier"Insurance brokers must promote a culture in which they act in their customers' best interests and provide them with the information they need to make an informed decision. This is central to the relationship between the industry and its customers," said the FCA's Mark Steward."It is also unacceptable that firms hold themselves out as independent when they are not."Bluefin agreed to settle at an early stage of the investigation, securing a 30 per cent reduction in the overall fine. Without this, it would have been lumped with a £5.75m payment.Read more: City watchdog accuses four asset managers with a total of more than £121bn under management of breaking competition lawThe watchdog said the FCA could have implemented systems and controls to manage the conflict arising from its Axa ownership. Instead, it did not disclose its policy of trying to push business with its parent and so customers could have been misled that the broker was unbiased.The FCA emphasised it was not criticising any other member of the Axa Group except Bluefin.The shamed insurance broker is no longer part of the group, having sold to US giant Marsh & McLennan last year for £295m. Axa took an €82m (£70m) hit from the sale, but may be relieved now that the fine is at arm's length.Read more: Axa reveals the cost of Bluefin's sale to Marsh & McLennan