Chrissy29 , whenever you use chat ALWAYS request a copy of the conversation you just need to ask the BT end to set it up before you clear down the chat. That way you have proof of what you advised BT and their response.
The question is why were you charged for the engineer visit? If it's for the main socket problem you mentioned, then they will charge for that,
You only get charged for the main socket if it is your fault see this http://bt.custhelp.com/app/answers/detail/a_id/12439/kw/engineer%20charges/c/345,353