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[Abridged] We carried out optical polarimetry of five dense cores, (IRAM04191, L1521F, L328, L673-7, and L1014) which are found to harbour VeLLO. Thisstudy was conducted mainly to understand the role played by the magnetic fieldin the formation of very low and substellar mass range objects using opticalpolarisation. The angular offsets between the envelope magnetic field direction(inferred from optical polarisation measurements) and the outflow positionangles from the VeLLOs in IRAM 04191, L1521F, L328, L673-7, and L1014 are foundto be 84$^\circ$, 53$^\circ$, 24$^\circ$, 08$^\circ$, and 15$^\circ$,respectively. The mean value of the offsets for all the five clouds is$\sim37^\circ$. If we exclude IRAM 04191, the mean value reduces to become$\sim25^\circ$. In IRAM 04191, the offset between the projected envelope andthe inner magnetic field (inferred from the submillimetre data from SCUPOL) isfound to be $\sim68^\circ$. The inner magnetic field, however, is found to benearly aligned with the projected position angles of the minor axis, therotation axis of the cloud, and the outflow from the IRAM 04191-IRS. We discussa possible explanation for the nearly perpendicular orientation between theenvelope and core scale magnetic fields in IRAM04191. The angular offsetbetween the envelope magnetic field direction and the minor axis of IRAM 04191,L1521F, L673-7, and L1014 are 82$^\circ$, 60$^\circ$, 47$^\circ$, and55$^\circ$, respectively. The mean value of the offsets between the envelopemagnetic field and the minor axis position angles for the four cores is foundto be $\sim60^\circ$. The results obtained from our study on the limited sampleof five cores with VeLLOs show that the outflows in three of them tend tonearly align with the envelope magnetic field.

Magnetic field structure around cores with very low luminosity objects