No I don't believe so, because it is so clearly a problem created by the previous owner. However since the cracks have shifted recently, there is no harm in trying a claim. I think you will find the insurer will process it, sending out a surveyor to assess it, then conclude that you as the houseowner should have taken greater steps to assess the structure of the property yourself.
The only possible other recourse you might have to claim is against the solicitor who assisted in your purchase. In the last few years it has now become a standard practice for the buyer's solicitor to ask questions about both Planning Consent for additions and Building Control approval for modifications that form part of the Building Control Regulations. It is this latter one that you are interested in because the modifications that you mention definitely required Building Control approval, your seller didn't get it (and wouldn't have got it anyway - structurally this does not met the Regulations - however that doesn't mean it is necessarily unsafe).
When solicitors starting asking about this as a standard question, I don't know - but it came about because buyers were making claims against solicitors because the lack of such approva;ls and because of the problems being found afterwards.
Write to that solicitor, asking for copies of the completed 'Standard Enquiries before Contract', - if you didn't retain them when you moved in or weren't supplied with them. Don't say why you want them - then work out whether this question about Building Control approval was asked or not.