When people greet us by 'howdy howdy', what is the best reply to it? Is it also used in British English?
Howdy is a contraction of "howdy do", which is itself a (primarily south US) contraction of "how do you do", which is a synonym for hello.
For this reason, any standard response to "hello" is a valid response to "howdy":
how are you?
how you doin'? (esp. NY)
"Howdy howdy" is a jovial form of "howdy", and hence (as StoneyB alluded in a slightly tongue-in-cheek way above), it would be acceptable to respond in a similarly jovial manner, such as
How've ya been?
Yo! How ya' doin!