If a letter starts with Dear Sir what should it be signed off as?

Yours faithfully is used if the letter is addressed Dear Sir or Dear Madam (never Dear Sir/Madam unless you want to look like junk mail). Yours sincerely is used if the letter is addressed Dear Mr Smith (or Mrs Smith). See: http://www.debretts.co.uk/forms-of-address.aspx for all the details you will ever need on this subject.