The 41-year-old actor, who shot to prominence as Tim in Ricky Gervais's The Office and has been in the public eye in the UK for more than 10 years, admitted that he's not ready to embrace the fame game.
"People have been annoying me in restaurants for a long time, and now it'll just be all over the world. Yippee," he said.
"I'm getting a glimpse of that external reaction to it now, the nearer the film gets to release. I mean that level of fame obviously is something very different to what most people will get to experience, but my life doesn't feel any different yet."
Sherlock star Martin, who stars as hobbit Bilbo Baggins in the first instalment of Peter Jackson's Lord Of The Rings prequel, describes himself as "a very, very private person". He doesn't want his two kids with long-term partner Amanda Abbington to see him as anything other than their dad.
"I want to keep my children absolutely out of it until they're of an age where they can decide," he said.
"Sometimes when I'm stopped in the street and I'm with my children, I always try and get them out of the picture and they'll go, 'Why don't you want us?' and I'm like, 'No, I'm protecting you!'."
:: The Hobbit is out now.