I got a 30 day stamp in my UK passport at a border crossing. Can I go to the local immigration office and get that extended for another 30 days or do I have to leave the country and come back in to get another 30 days?

I assume you're asking about an extension in Thailand, I'll move your question to the correct forum. 

You can go to imm and obtain 30day extension 1900baht

You can obtain a single extension of 30 days at your local Immigration Office for 1900 baht, best done in the last week. 

cheers guys