Once convictions are 'spent' (as defined by the Rehabilitation of Offenders Act), you never have to declare them at any time, except for an application which is covered by an exemption under the Act (such as an application to work with children or vulnerable adults).
No domestic insurance policies are covered by any exemptions under the Act, so therefore spent convictions do not have to be divulged. Even if a question is worded as "Have you ever been convicted . . .?", you can lawfully answer 'No'. Doing so could not invalidate any claim.
However, there's a grey area regarding the question "Have you ever been refused cover?". Someone might apply for insurance, before their conviction is spent, and be turned down. Later, when their conviction is spent, they can answer 'No' to the convictions question but it seems that they'd still have to answer 'Yes' to the refusals question, giving the reason as 'criminal conviction - now spent'. (i.e. they wouldn't be obliged to provide any details about the conviction).
Insurance companies have no direct access to criminal records but they do work closely with police fraud teams and also employ staff to 'ask questions' about claims.
http://www.lawontheweb.co.uk/rehabact.htm
Chris