We moved into our current house in May 2014. However in October 2015, my partner had a mini breakdown and as a result ended up with 2 criminal convictions, both resulted in fines. My question is should we have informed the landlord, as i recently read it can affect their buildings insurance if something happened. It's a bit of a grey area as we live in Northern Ireland where it is not spent for 5 years, but in England and Wales it is already spent.
Any advice would be greatly appreciated.

As you say, the law is different in Northern Ireland, but the general principle in England & Wales is that if the landlord or letting agent asks, you have to disclose. It might be worth checking your tenancy agreement, but if it's in there, they would probably have asked you before you signed it. The best source of advice would probably be NIACRO. You can find their contact details here.

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If you are to punish a man retributively you must injure him. If you are to reform him you must improve him. And men are not improved by injuries. (George Bernard Shaw)

We were never asked at the time, and my partner didn't have the record at the time, checked the tenancy agreement nothing in there either.

Again, the rule over here is that if they don't ask you, you don't have to tell them. If there's nothing in the tenancy agreement, then they can't be that worried about it. It might be worth checking with NIACRO, though, as they might know something about the law in Northern Ireland that wouldn't apply in England.

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If you are to punish a man retributively you must injure him. If you are to reform him you must improve him. And men are not improved by injuries. (George Bernard Shaw)