It says that there is insufficient evidence to justify continuing the inquiry.
The move follows the SFO’s abandonment of its investigation of property magnates Robert and Vincent Tchenguiz, both of whom had been closely involved with Kaupthing.
Vincent Tchenguiz had borrowed £100m from the bank shortly before it collapsed; both brothers have always denied any wrong-doing.
In the run-up to its collapse in October 2008 with debts of $50bn (£31bn), the bank, which was Iceland’s largest, was haemorrhaging funds. In December 2009, the SFO announced it was opening an investigation into suspected fraud offences committed within the UK jurisdiction in relation to the bank.
The SFO says that it will continue its close co-operation with the Special Prosecutor’s Office in Reykjavik.