Detections of transiting planets from the upcoming PLATO mission are expected to face significant contamination from contaminating eclipsing binaries, resulting in false positives. To counter this, a ground-based programme to acquire time-critical photometry is pursued. Its principal aim is to obtain time-series observations of the planet candidate and its surrounding stars at the times of expected transits. This programme is part of the PLATO Ground-based Observations Programme, which also covers spectroscopic and imaging observations. The current photometric follow-up programme is assembling the required observational resources, executing benchmark observations, and defining strategies for the observations and their reporting. Post-launch, it will focus on coordinating photometric data collection and analysis, and will update candidate statuses in the PLATO follow-up database. Its work packages are outlined, covering specific tools, citizen contributions, standard and multi-colour observations, secondary eclipses, and reprocessing of archival photometry. Ground-based follow-up photometry will likely concentrate on longer-period candidates, given that false positives of short-period candidates will likely become identifiable in timeseries available from GAIA in the near future. Geographical considerations for follow-up observations from the first PLATO long-observation field LOPS2 are outlined, which lies in the southern hemisphere, with later fields expected to be more suitable for northern observers.