We present millimetre ( SMA ) and sub-millimetre ( SCUBA-2 ) continuum observations of the peculiar star KIC 8462852 which displayed several deep and aperiodic dips in brightness during the Kepler mission . Our observations are approximately confusion-limited at 850 \mu m and are the deepest millimetre and sub-millimetre photometry of the star that has yet been carried out . No significant emission is detected towards KIC 8462852 . We determine upper limits for dust between a few 10 ^ { -6 } M _ { \oplus } and 10 ^ { -3 } M _ { \oplus } for regions identified as the most likely to host occluding dust clumps and a total overall dust budget of < 7.7 M _ { \oplus } within a radius of 200 AU . Such low limits for the inner system make the catastrophic planetary disruption hypothesis unlikely . Integrating over the Kepler lightcurve we determine that at least 10 ^ { -9 } M _ { \oplus } of dust is required to cause the observed Q16 dip . This is consistent with the currently most favoured cometary breakup hypothesis , but nevertheless implies the complete breakup of \sim 30 Comet 1/P Halley type objects . Finally , in the wide SCUBA-2 field-of-view we identify another candidate debris disc system that is potentially the largest yet discovered .