You can lawfully answer 'No' in respect of any criminal convictions which are now spent. You can also lawfully answer 'No' in respect of any refusal of insurance where that refusal was solely because of a criminal conviction which is now spent:
http://www.lawonthewe...tion_of_Offenders_Act
Any matter which was dealt with by a fixed penalty (e.g. speeding), rather than by an appearance before a court, does not constitute a 'conviction', so there is no need to declare it. However any matter where a person pleads guilty (or is found guilty) by a court, constitutes a criminal conviction, which must be declared (unless that conviction is now spent, as above).
It's a standard condition of most (and probably all) insurance policies that the insured person must immediately notify the insurer of any change to the validity of the declarations which were made when the policy was taken out.
Chris