I'm completely baffled by the responses on here!!!
When OP and her husband split up they agreed that until their child reached adulthood, she would still be insured for health problems.
This makes complete sense to me. Waiting times are at an all time high with the NHS, and if you have something non urgent, but debilitating, like a need for a hip op, that is a long time to be impaired. It is in her ex hubands interest that, whilst, she is providing care for their child, and until the child is an adult, that she has health cover to protect her.
The OP, knowing this was the agreement, went ahead and used the insurance. After which she was told it was no longer in force. If the OP had know she was not insured, she may have decided she did not have the funds to cover the investigations. Similarly, she might have decided to take out health insurance for herself, if she had been informed she was not insured.
If I was the OP I would be really angry about the breach of the agreement and the very difficult position she has been put in.. .She may not have anything in writing from her ex husband, but she does have proof of the cancellation mid term, her behaviour which showed she clearly had the impression she was covered, and the 'backdating' issue which is legally extremely dodgy. You can't notify someone you have ended a contract and ask them to consider it ended at a date prior to notification(!)
OP I would argue firstly that you were covered at the time you initiated the investigations (and 'backdating' the policy cancellation would not therefore remove the insurance companines liability. Secondly that your ex husband has reneged on a verbal agreement to cover you (presumably the existence of the policy running until recently supports this) and absolutely do not back down. Take it to the insurance ombudsman if necessary.
I would suggest to the ombudsman that the policy was not cancelled until notification was received by the ex husbands company that a claim was in progress, and the backdating was done in an attempt to avoid paying this claim, as that seems to be the most likely explanation here. If so they are legally liable to pay the entire claim, including the OP.