I would advise any residents association that is anything other than a purely representative organisation i.e. doing minor maintenance, grass cutting, social events etc. to have Public Liability including member to member insurance. You cannot hold someone else responsible for your actions, so someone elses insurance will not cover you in every situation. Your organisation is only covered by insurance if it has its own insurance or is specifically named on an insurance policy. It is also possible that if the common areas are owned by a development company (or even local authority), they may ask to be indemnified by you. The cost of PL insurance for small organisations is quite cheap, so better to have it just in case as the alternative is for the trustees of the Association to be liable for any claims.