Ultra high energy neutrinos are important astrophysical messengers that carry information on processes taking place in extreme astrophysical environments. The detection of neutrinos originating from the Greisen-Zatsepin-Kuzmin (GZK) process would confirm the proton dominance in the composition of the Ultra High Energy Cosmic Rays (UHECRs) as well as help to identify the unknown sources of the charged particles. Data taken between April 2008 and May 2009 by the IceCube neutrino observatory in its 40 strings configuration were used for an all-flavour GZK neutrino event search. The main challenge for this search was the separation of the faint GZK neutrino signal (order of 1 event per year) from the several orders of magnitude higher atmospheric muon background. Special focus was given to identifying the topological differences between signal and background events and, based on them, the development of new background rejection techniques. High energy events have been pre-selected by requiring a minimum amount of detected light and number of active photomultipliers in an event. Photon hits in IceCube’s surface array photomultipliers were used to identify and reject atmospheric muon background events. Photon hit pattern differences (in time and space) in the in-ice detector between background and signal events were used to construct new cut parameters for background rejection. UHE neutrino events were selected by a final analysis cut determined by optimising the Model Discovery Potential parameter (MDP) based on the neutrino flux from a reference GZK model. The predicted rates for the analysis live time of 315.34 days were 0.32 signal neutrino events and a total background rate of 0.015. The achieved least detectable signal by the analysis is 5.3 events which gives MDP=16.4. This means a normalisation factor of 16.4 higher on the reference GZK neutrino flux would be necessary in order to be able to claim a 5σ discovery. The full data sample was processed after the analysis methodology had been frozen and approved by the IceCube collaboration. No data events survived the analysis’ final cuts. A 90% confidence level upper limit was calculated based on the null observation giving E 2 φ ≤ 4.75 × 10−8 GeV cm−2 s−1 sr−1 in the energy range [105.5 , 109 ] GeV, a result slightly below the Waxman-Bahcall limit.