If a conviction is spent you do not have to answer Yes. If it is unspent and you answer yes, I'm not aware of any mainstream insurer who will provide Buildings and Contents cover. Several, including LV=, will provide car insurance if you only have unspent non-motoring convictions.
The good news is that there is a long list of brokers available on the Unlock website who will arrange insurance for you (ironically quite often underwritten by different arms of the same mainstream insurers who won't deal with you directly...
The only issue is cost - your unspent conviction adds an unhealthy amount to the premium.
There is also an online insurer who specialises in people with convictions and has been advertising/sponsoring an Unlock page (homeprotect.co.uk)
Link here: Home Protect