Many transient and variable sources detected at multiple wavelengths are also observed to vary at radio frequencies. However, these samples are typically biased towards sources that are initially detected in wide-field optical, X-ray or gamma-ray surveys. Many sources that are insufficiently bright at higher frequencies are therefore missed, leading to potential gaps in our knowledge of these sources and missing populations that are not detectable in optical, X-rays or gamma-rays. Taking advantage of new state-of-the-art radio facilities that provide high quality wide-field images with fast survey speeds, we can now conduct unbiased surveys for transient and variable sources at radio frequencies. In this paper, we present an unbiased survey using observations obtained by MeerKAT, a mid-frequency (∼1.4 GHz) radio array in South Africa's Karoo Desert. The observations used were obtained as part of a weekly monitoring campaign for X-ray binaries (XRBs) and we focus on the field of MAXI J1820+070. We develop methods to optimally filter transient and variable candidates that can be directly applied to other datasets. In addition to MAXI J1820+070, we identify four likely active galactic nuclei, one source that could be a Galactic source (pulsar or quiescent X-ray binary) or an AGN, and one variable pulsar. No transient sources, defined as being undetected in deep images, were identified leading to a transient surface density of < 3.7 × 10 −2 deg −2 at a sensitivity of 1 mJy on timescales of one week at 1.4 GHz.