Reviews of a new Flight of the Conchords tour are proving the iconic Kiwi duo have still got it - but Kiwis may be missing out on their new tunes.

Jemaine Clement and Bret McKenzie have begun a new UK tour with a run of shows at London's Soho theatre, and reception has been incredibly positive, with The Guardian givign the duo a five-star review.

"The pair prove with plenty to spare that when it comes to silly and sophisticated comic songwriting, there's still no one to touch them," wrote critic Brian Logan.

The duo are performing a number of brand-new songs, which Logan said "easily scale the dizzy heights of their best work."

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The Soho shows all sold out "without a shred of publicity," wrote Logan.

Empire magazine features editor Nick de Semlyen said the show was "amazing".

"Flight Of The Conchords playing mostly new material, at times hilariously shambolically, in a tiny room, accompanied by a one-man New Zealand Symphony Orchestra. I had a smile on my face the entire time."

The duo's UK tour finishes in April. No New Zealand shows have been announced as of yet.