All reputable electricians should have proper insurance. Checking this is key to ensuring you choose the right electrician. You should be looking for public liability insurance and professional indemnity insurance as a minimum as these cover the kinds of risks that your home or buildings insurance might not.
Public liability insurance provides cover for any accidents that might happen whilst the electrician is at your home or office. For example, if they leave a trailing cable and someone gets hurt falling over it, their insurance should cover any compensation that's owed. Professional indemnity cover is there for any errors that cause damage to your property, for example, if there's a fire.