Justices of the Peace are accustomed to having members of the public in their homes. One of the questions asked during the nomination process is about this and whether they have a suitable place within their home to conduct their business.
Some Justices of the Peace will be happy to see you at their workplace.
Some areas run 'JP signing centres' or 'JP service desks' - to see if there's one in your area you can check on this website in theservice centre section or contact the Association Registrar.