The formation and evolution of extremely low-mass stars is at present poorly understood. Having masses much smaller than the typical observed and predicted collapsing mass of protostellar environments, there has been controversy as to whether field brown dwarfs form from turbulent collapse directly, or as embryos ejected from nascent multiple systems. The aim of this research is to shed light on the formation and evolution of brown dwarfs using a recently-developed interferometric image post-processing technique called kernel phase interferometry. This makes use of self-calibrating observables which are robust against small wavefront errors from turbulence or instrumental aberrations, achieving higher contrast and angular resolution than is possible with other approaches. The study of ultracool dwarf binaries is therefore also a test case for resolving much fainter planetary companions in future surveys. In this talk, I present a re-analysis of archival Hubble Space Telescope (HST) snapshot images of nearby L dwarfs using kernel-phase interferometry. This new study reveals five new detections of dwarf companions, precise astrometry on known binaries in the sample and detection constraints on possible high-contrast companions.