The EU is a guarantor of peace in Europe by bringing its countries closer together and overcoming the disputes of the past.
Europe has enjoyed its longest period of peace since the formation of international confederations such as the EU.
Since UK citizens have voted against these gains, it is not important that these gains exist. They are not seen as worth the costs of EU membership.
It is highly unlikely that European countries will fight each other merely because they are not members of the same particular group - the EU.