I am an English businessman.
The way you're supposed to sign off a letter depends on how you start.
In a letter, if you don't know the name of the person to whom you are sending the letter, you start "Dear Sirs,". If you start with this form, it is correct to end with "Yours faithfully,"
In a letter, if you do know the name of the person to whom you are sending the letter, you start "Dear Mark,". If this is a formal letter, then it is correct to end with "Yours sincerely," - though if this is an informal letter you can end it however you want.
With email the conventions are more recent and less clearly defined. I often start with "Hi Mark", or "Hello Mark" (just "Mark," is a bit gruff) if I've already spoken with the addressee. Most emails to me usually follow this format. I usually end these emails with "Kind regards," though lots of people just use "Regards,"
I do use the "Dear Mark, / Yours Sincerely" format in emails if I'm making contact with someone for the first time.
Hope this helps...