I am a resident in the uk and own a holiday home in the harz. Am I liable for zweitwohnungsteuer?

No precise answer possible. Each commune has their own regulations.

Braunlage?

They are now asking I pay back to 2009. However, I visited the town hall in sankt andreasberg in 2010 and 2011 and was told I do not need to pay. Do I need to visit a lawyer.

Since first of november 2011 Sankt Andreasberg belongs to the city Braunlage. I think, you will have to pay, at least at 01012013 – with or without lawyer.