Context. The Orion Kleinmann-Low nebula (Orion-KL) is a complex region of star formation. Whereas its proximity allows studies on a scale of a few hundred AU, spectral confusion makes it difficult to identify molecules with low abundances. Aims: We studied an important oxygenated molecule, HCOOCH3, to characterize the physical conditions, temperature, and density of the different molecular source components. Methyl formate presents strong close rotational transitions covering a wide range of energy, and its emission in Orion-KL is not contaminated by the emission of N-bearing molecules. This study will help in the future 1) to constrain chemical models for the formation of methyl formate in gas phase or on grain mantles and 2) to search for more complex or prebiotic molecules. Methods: We used high-resolution observations from the IRAM Plateau de Bure Interferometer to reduce spectral confusion and to better isolate the molecular emission regions. We used twelve data sets with a spatial resolution down to 1.8″ × 0.8″. Continuum emission was subtracted by selecting apparently line-free channels. Results: We identify 28 methyl formate emission peaks throughout the 50″ field of observations. The two strongest peaks, named MF1 and MF2, are in the Compact Ridge and in the southwest of the Hot Core, respectively. From a comparison with single-dish observations, we estimate that we miss less than 15% of the flux and that spectral confusion is still prevailing as half of the expected transitions are blended over the region. Assuming that the transitions are thermalized, we derive the temperature at the five main emission peaks. At the MF1 position in the Compact Ridge we find a temperature of 80 K in a 1.8″ × 0.8″ beam size and 120 K on a larger scale (3.6″ × 2.2″), suggesting an external source of heating, whereas the temperature is about 130 K at the MF2 position on both scales. Transitions of methyl formate in its first torsionally excited state are detected as well, and the good agreement of the positions on the rotational diagrams between the ground state and the vt = 1 transitions suggests a similar temperature. The LSR velocity of the gas is between 7.5 and 8.0 km s-1 depending on the positions and column density peaks vary from 1.6 × 1016 to 1.6 × 1017 cm-2. A second velocity component is observed around 9-10 km s-1 in a north-south structure stretching from the Compact Ridge up to the BN object, and this component is warmer at the MF1 peak. The two other C2H4O2 isomers are not detected, and the derived upper limit for the column density is ≤3 × 1014 cm-2 for glycolaldehyde and ≤2 × 1015 cm-2 for acetic acid. From the 223 GHz continuum map, we identify several dust clumps with associated gas masses in the range 0.8 to 5.8 M&sun;. Assuming that the methyl formate is spatially distributed as the dust is, we find relative abundances of methyl formate in the range ≤0.1 × 10-8 to 5.2 × 10-8. We suggest a relation between the methyl formate distribution and shocks as traced by 2.12 μm H2 emission. Based on observations carried out with the IRAM Plateau de Bure Interferometer. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain).A fits image of the HCOOCH3 integrated intensity map (Fig. 4) is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/532/A32. All spectra can be obtained upon request to the authors.Table 10 and Appendix A are available in electronic form at http://www.aanda.orgRead less <