Looks to me as if HFC have been receiving payments from Ins.Co. but not marrying them up with your account. If Ins.Co. did not quote the correct reference the payments might be festering in a suspense account at HFC. The HFC system would read 'no payments' to the account and that would trigger off the account default programme.
Is the date of the default soon after Ins.Co. started making payments on your behalf?
Ask Ins.Co. how they have been making payments and what reference they used, so that you can inform HFC.
I would either call HFC and ask to speak to a supervisor or manager, or write to them explaining what has happened.
This sounds like you are doing their job for them, but sometimes it's the ony way!
If you can get them to agree that they have been receiving the payments, then you should be able to persuade them to remove the default.
Elsinore